Quantitative Methods-II (MB152): April 2006

Quantitative Methods-II (MB152): April 2006

• Answer all questions.
• Marks are indicated against each question.
1. In a family there are three children, what is the probability that the family has no male child?
(a)
1
8 (b)
3
8 (c)
2
8 (d)
1
7 (e)
3
7 .
(2 marks)
< Answer >
2. A person’s pocket contains 5 fifty paise coins, 4 twenty paise coins and 4 ten paise coins. A boy is asked to draw two
coins at random. What is the probability that the boy can draw the maximum possible amount?
(a) 0.653 (b) 0.128 (c) 0.753 (d) 0.556 (e) 0.364.
(1 mark)
< Answer >
3. Maruti Udyog has 20 persons working in output section. Out of them, there are 11 men and 9 women. One-day 7of
them are promoted to another section. Find what is the probability that 4 of the promoted ones are women? (Use
Hypergeometric distribution).
(a) 0.2312 (b) 0.2682 (c) 0.3257 (d) 0.4372 (e) 0.3178.
(2 marks)
< Answer >
4. There are two packs of cards from which one card is drawn at random. What is the probability that both of them are
red?
(a) 1 (b) 1/2 (c) 1/3 (d) 1/4 (e) 1/13.
(2 marks)
< Answer >
5. Three dice are cast at a time. What is the probability of getting a sum total of 12?
(a)
15
216 (b)
17
216 (c)
19
216 (d)
23
216 (e)
25
216 .
(1 mark)
< Answer >
6. The observations from a simple random sample are given below:
51 25 20 7 35 15
It is known that the population is normally distributed. If an interval estimate of the population mean is to be made on
the basis of the given information, then which of the following probability distributions will be most appropriate for
making the interval estimate?
(a) Chi-square distribution
(b) Normal distribution
(c) t-distribution with 5 degrees of freedom
(d) t-distribution with 6 degrees of freedom
(e) F-distribution.
(2 marks)
< Answer >
2
7. There are 600 business students in the graduate department of a university and the probability for any student to need
a copy of a particular textbook from the university library on any day is 0.05. The students draw the books from the
library independently.
What is the mean number of copies required on any day?
(a) 28 (b) 29 (c) 30 (d) 31 (e) 32.
(1 mark)
< Answer >
8. Two unbiased dice are cast, then the probability that the total of the numbers on the dice is any number from 2 to
12(both inclusive) is
(a) 0 (b) 1 (c) 1/6 (d) 5/12 (e) 5/6.
(1 mark)
< Answer >
9. On the average, one in 400 items is defective. If the items are placed in boxes of 100 each, then what is the probability
that none of the boxes will contain defectives? (Use Poisson distribution).
(a) 0.3344 (b) 0.5566 (c) 0.7788 (d) 0.8899 (e) 0.9999.
(2 marks)
< Answer >
10. A factory produces blades in packets of 10 each. The probability that a blade to be defective is 0.2%. Find the number
of packets having two defective blades in a consignment of 10,000 packets. (Use Poisson distribution).
(a) 1 (b) 2 (c) 3 (d) 4 (e) 5.
(2 marks)
< Answer >
11. The graph of which of the following distributions is flat?
(a) t-distribution (b) Normal distribution
(c) Continuous uniform distribution (d) Chi-square distribution
(e) F-distribution.
(1 mark)
< Answer >
12. Given that the mean of a binomial distribution is 20 and the standard deviation is 4. Find out the number of trials.
(a) 50 (b) 70 (c) 90 (d) 100 (e) 120.
(1 mark)
< Answer >
13. Z is a binomial random variable. For 25 trials the standard deviation of Z is 6 . What will be the standard deviation
of Z for 75 trials?
(a) 6 (b) 6 (c) 3 2 (d) 18 (e) 9 2.
(2 marks)
< Answer >
14. The probability that a continuous random variable will assume a particular value is
(a) Zero (b) Between 0 and 0.50
(c) Between 0.50 and 1.00 (d) Equal to 0.50
(e) Unknown.
(1 mark)
< Answer >
15. A box contains 60 ballpoint pens out of which 10 pens are defective. 8 pens are randomly picked from the box. The
probability distribution of the number of pens found to be defective out of the pens which are randomly picked, will
be
(a) A discrete Uniform distribution
(b) A Binomial distribution
(c) A Hypergeometric distribution
(d) A Chi-square distribution
(e) An unknown distribution.
(1 mark)
< Answer >
3
16. When sampling without replacement is done from a finite population such that, the probability of success is not
constant from trial to trial, then it follows the
(a) Binomial distribution (b) Uniform distribution
(c) Normal distribution (d) Continuous distribution
(e) Hypergeometric distribution.
(1 mark)
< Answer >
17. The concept of sampling distribution applies to
(a) Only discrete probability distributions from which random samples are obtained
(b) Only continuous probability distributions from which random samples are obtained
(c) Any probability distribution from which random samples are obtained
(d) Only normal probability distributions
(e) Only binomial distributions.
(1 mark)
< Answer >
18. A sample of size 16 yielded a mean of 10. The population mean is known to be 12. What is the expected value of the
sampling distribution of mean?
(a) 10 (b) 12 (c) 2.5 (d) 3.0 (e) 1.732.
(2 marks)
< Answer >
19. A researcher is studying the number of trees that contain a certain type of locust in the Smoky Mountains each year.
He has found that in a year an average of 25% of the trees contain the locust with a standard deviation of 4%. If 100
trees were randomly sampled, which of the following statements about the sampling distribution of mean is
incorrect?
(a) The standard deviation of the distribution of sample means is 4%
(b) The mean of the distribution of sample means is 25%
(c) The standard deviation of the distribution of sample means is 0.40%
(d) The shape of the distribution of sample means is approximately normal
(e) The variance of the distribution of sample means is 0.16%.
(1 mark)
< Answer >
20. If we consider the process of selecting a simple random sample as an experiment then which of the following can be
treated as random variable(s)?
I. Sample mean.
II. Sample standard deviation.
III. Sample range.
IV. Sample median.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Only (IV) above
(e) All (I), (II), (III) and (IV) above.
(1 mark)
< Answer >
21. When estimating the population mean from a sample taken from a normal population with unknown variance, the t
distribution may be used with number of degrees of freedom equal to
(a) Sample size (b) Sample size + 1
(c) Sample size – 1 (d) 0 (e) 1.
(1 mark)
< Answer >
22.
If the population is normally distributed then for any given sample size, the sampling distribution of
x
s
n
− μ
is
(a) A normal distribution
(b) The standard normal distribution
(c) A t-distribution
(d) A t-distribution only when the sample size is 30 or less
(e) A t-distribution only when the sample size is more than 30.
(1 mark)
< Answer >
4
23. For the following information assume that the population is normal and that a test for the population mean is required
with the given null hypothesis:
n = 16
H0 : μ = 15
x = 16
σ2 = 16
Which of the following statements is correct?
(a) The test statistic = 0.50 and it will follow the standard normal distribution if H0 is true
(b) The test statistic = 0.25 and it will follow the standard normal distribution if H0 is true
(c) The test statistic = 1.00 and it will follow the standard normal distribution if H0 is true
(d) The test statistic = 1.00 and it will follow the t distribution with 16 degrees of freedom if H0 is true
(e) The test statistic = 1.00 and it will follow the t distribution with 15 degrees of freedom if H0 is true.
(1 mark)
< Answer >
24. Which of the following can be used for knowing the test statistic in hypothesis tests?
I. The sample mean, when the test involves the population mean.
II. The difference between two sample means, when the test involves the difference between two population means.
III. The sample proportion, when the test is about the population proportion.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Both (I) and (II) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
25. The following details are available for a hypothesis test on population proportion:
H0: p = 0.60
H1: p ≠ 0.60
The standard error of proportion is 0.03098. What is the sample size? (Round off your answer to the nearest integer)
(a) 100 (b) 250 (c) 19 (d) 625 (e) 417.
(1 mark)
< Answer >
26. In which of the following ways can binomial trials be performed on a finite population with specific numbers of
successes and failures?
(a) By sampling without replacement
(b) By sampling with replacement
(c) By adding a constant to the number of successes obtained in a given number of trials
(d) By deducting a constant from the number of successes obtained in a given number of trials
(e) By multiplying a constant to the number of successes obtained in a given number of trial.
(1 mark)
< Answer >
27. For a sample randomly collected from a population, the following details are available:
Σx2 = 1840
Σx = 160
Number of observations = 16
What is the estimated standard error of mean?
(a) 1 (b) 2 (c) 4 (d) 10 (e) 16.
(2 marks)
< Answer >
28. In which technique of random sampling the first element of the sample is randomly selected from the population and
the remaining elements are selected at uniform intervals that are measured in time, order or space?
(a) Simple random sampling (b) Stratified sampling
(c) Cluster sampling (d) Systematic sampling
(e) Judgmental sampling.
(1 mark)
< Answer >
5
29. How will the standard error of mean be affected if the sample size is reduced?
(a) It will decrease (b) It will remain unchanged
(c) It will increase (d) It will change unpredictably
(e) It will be equal to the population variance.
(1 mark)
< Answer >
30. The following details are available with regard to a hypothesis test on population mean:
H0: μ = 9
H1: μ ≠ 9
n = 25
σ2 = 256
x =15
Significance level = 0.05
The population is normally distributed. It is later known that the true population mean is 9.
Which of the following can be said with regard to the test?
(a) There is insufficient information for doing the test
(b) The t distribution should be used
(c) The test does not lead to either type I or type II error
(d) The test leads to a type I error
(e) The test leads to a type II error.
(2 marks)
< Answer >
31. Which of the following is the correct test statistic to use in testing the difference between the means of two normally
distributed populations with equal and unknown variances, using small, independent random samples?
(a) t-statistic (b) z-statistic
(c) F-statistic (d) Chi-square statistic
(e) Mean of the two sample means.
(1 mark)
< Answer >
32. The following details are available with regard to a hypothesis test on difference between means of two populations:
n1 = 64 1 Σx = 320
n2 = 36 2 Σx = 144
The value of the test statistic is 0.70796 and the standard error of difference between means is 2.825. The samples
collected from the two populations are independent. What is the value of 1 2 μ − μ according to the null hypothesis?
Round off your answer to the nearest integer.
(a) 1 (b) –1 (c) 0 (d) 2 (e) – 2.
(1 mark)
< Answer >
33. Which of the following is indicated if the standard error of estimate for a regression equation is zero?
(a) The standard deviation of the observed values of the dependent variable is zero
(b) The standard deviation of the independent variable is zero
(c) The observed value of the dependent variable will always be equal to its estimated value, for a given value of the
independent variable
(d) There is no correlation between the variables involved
(e) The correlation coefficient between the variables is greater than zero but less than 1.
(1 mark)
< Answer >
34. The standard deviation of the sampling distribution of the mean is also called the
(a) Standard error of the mean (b) Sum of squares
(c) Sum of squared deviations (d) Variance
(e) Sample standard deviation.
(1 mark)
< Answer >
6
35. In a test of hypothesis for a population mean it is found out that the test statistic is equal to 1.60. The sample mean is
48 and the standard error of mean is 5. What is the value of the population mean according to the null hypothesis?
(a) 8 (b) 88 (c) 56 (d) 40 (e) 43.
(1 mark)
< Answer >
36.
Suppose in a sample of 30 people, the mean height ( x ) was observed to be 68 inches and the standard deviation (σ) =
2, then the 95% confidence interval for μ is
(a) (66.8246, 71.4522) (b) (67.2843, 68.7156)
(c) (65.2965, 70.2587) (d) (66.2543, 69.0256)
(e) (65.2563, 70.2915).
(1 mark)
< Answer >
37. Which of the following is true?
(a) The mean of the sampling distribution of the mean depends on the sample size
(b) The probability of making a Type I error is lesser in a one-tailed test than a two-tailed test for a given
significance level
(c) The standard deviation of the sampling distribution of mean depends on the sample size
(d) The calculation of the z-statistic in a hypothesis test always requires the standard deviation of the sample
(e) If the value of the test statistic falls in the critical region then the null hypothesis is accepted.
(1 mark)
< Answer >
38. The following details are available with regard to a hypothesis test on means of two populations:
n1 = 64 2
1 σ = 256
n2 = 36
The standard error of difference between means is 8 and the samples collected from the two populations are
independent.
What is the standard deviation of the second population?
(a) 2 (b) 4 (c) 8 (d) 12 (e) 144.
(2 marks)
< Answer >
39. In hypothesis testing, if the level of significance is made smaller, then the rejection region
(a) Becomes larger
(b) Becomes smaller
(c) Remains the same
(d) Becomes equal to the acceptance region
(e) Becomes larger than the acceptance region.
(1 mark)
< Answer >
40. City Finance Company Ltd. is a non-banking finance company. In the recent years there has been variations in the
demand for loans as well as in the rate of interest. The general manager of the company wants to know whether the
variations in the amount of advances explain the variations in the profit after tax of the company.
The following data pertain to the operations of the company in the recent years:
Year 2005 2004 2003 2002 2001 2000
Amount of advances (Rs.in crores) 7.0 5.5 5.0 4.5 4.0 4.0
Profit after tax (Rs. in lakhs) 54 48 42 27 19 14
What percentage of the variations in profit after tax is explained by the variations in the amount of advances?
(a) 84.31% (b) 15.69% (c) 91.82% (d) 8.18% (e) 10.15%.
(2 marks)
< Answer >
7
41. If a hypothesis is tested at a significance level of 10% then it means that
(a) There is a 10% probability that the null hypothesis will be rejected though it is true
(b) There is a 10% probability that the null hypothesis will be false
(c) There is a 10% probability that the null hypothesis will be true
(d) There is a 90% probability that the alternative hypothesis will be false
(e) There is a 90% probability that the alternative hypothesis will be true.
(1 mark)
< Answer >
42. Two variables X and Y, are related by a regression equation such that X is the independent variable and Y is the
dependent variable. The following details are available:
Coefficient of correlation between X and Y = 0.80
Standard deviation of X = 5
Standard deviation of Y = 8
The slope of the regression equation is
(a) 0.80 (b) 1.28 (c) 6.4 (d) 32 (e) 64.
(1 mark)
< Answer >
43. For a simple regression equation the following results were obtained:
If X = 5 then Yˆ = 31
If X = 10 then Yˆ = 47
Where X is the independent variable and ˆY is the estimated value of the dependent
variable Y.
ΣX = 60
Number of data points = 6
What is the mean of the observed values of the dependent variable Y?
(a) 15 (b) 32 (c) 47 (d) 18.2 (e) 25.
(1 mark)
< Answer >
44. A multiple regression equation has
(a) Multiple dependent variables
(b) One independent variable
(c) One dependent variable
(d) A standard error of estimate equal to zero
(e) A standard error of estimate equal to one.
(1 mark)
< Answer >
45. The covariance of a random variable with itself is always
(a) A positive quantity (b) A negative quantity
(c) Zero (d) Less than its expected value
(e) Less than its variance.
(1 mark)
< Answer >
46. The coefficient of correlation between variables X and Y is 0.80.
Cov (X, Y) = 20
σX = 5
What is the variance of Y?
(a) 5 (b) 20 (c) 25 (d) 50 (e) 100.
(2 marks)
< Answer >
8
47. The coefficient of variation of 5X is 20% and the coefficient of variation of 4Y is 40%.
μX = 30
Y μ = 50
Cov(X, Y) = 90
What is the coefficient of correlation between 4X and 5Y?
(a) 0.60 (b) 0.75 (c) 0.80 (d) 0.90 (e) 0.50.
(2 marks)
< Answer >
48. If the covariance of two random variables X and Y is equal to zero then it can be said that
(a) The random variables are dependent on each other
(b) The random variables have a positive correlation
(c) The random variables have a negative correlation
(d) The random variables are independent of each other
(e) The variances of the two random variables are always zero.
(1 mark)
< Answer >
49. The correlation coefficient between X and Y is 0.70. Let U = 2X + 10 and V = 5Y – 7
What is the coefficient of correlation between U and V?
(a) 0.14 (b) 0.35 (c) 0.70 (d) – 0.70 (e) – 0.14.
(1 mark)
< Answer >
50. The value of chi-square statistic can never be negative, because
(a) The difference between the observed and expected frequencies are always positive
(b) The differences between the observed and expected frequencies are always squared
(c) The observed frequency can never be negative
(d) The expected frequency can never be negative
(e) The expected frequency is always equal to the observed frequency.
(1 mark)
< Answer >
51. A simple regression relationship was developed between two variables X and Y, with X as the independent variable.
ΣY = 792 ΣY2 = 79144 ( )2 Σ Y −Yˆ = 200 n = 8
The coefficient of determination is
(a) 0.2717 (b) 0.7283 (c) 0.3731 (d) 0.2137 (e) 0.7863.
(1 mark)
< Answer >
52. Which of the following is true with regard to simple regression and correlation analysis?
(a) Regression analysis helps in finding out how well an equation for estimating one variable from another and
correlation describes the relationship between the two variables
(b) If the coefficient of correlation between two variables is close to zero, then there is a strong correlation between
the two variables
(c) If the slope of a regression equation is negative then, there is a direct relationship between the variables involved
(d) If the slope of a regression equation is positive then, the coefficient of correlation between the variables involved
is positive
(e) Correlation analysis is used to determine cause-effect relationship between the variables involved.
(1 mark)
< Answer >
9
53. Which of the following criteria is not applicable to decision-making under risk
I. Maximize expected return.
II. Maximize return.
III. Minimize expect regret.
IV. Knowledge of likelihood occurrence of each state of nature.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Only (IV) above
(e) All (I), (II), (III) and (IV) above.
(1 mark)
< Answer >
54. Which of the following statement(s) is/are true?
I. The decrease in the conditional profit when the stocked unit is not sold is called as marginal loss.
II. According to marginal analysis, the vendor should stock additional units until marginal profit is just equal to
marginal loss.
III. In decision making under uncertainty, a decision maker has insufficient information to assign a probability.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Both (I) and (II) above
(e) All (I), (II), and (III) above.
(1 mark)
< Answer >
55. In decision-tree model, when the result of taking a decision is uncertain, then the result is represented by
(a) A line (b) A triangle (c) A square (d) A circle (e) A rectangle.
(1 mark)
< Answer >
56. The owner of ABC company facing a typical problem, how many products should be made daily so as to maximize
the profit. The cost of making a product is Rs.20 and it sells for Rs.25. The owner has collected following data:
Demand(In units) 28 30 31
Probability of Demand 0.29 0.32 0.39
The expected profit with certainty for the given situation is
(a) Rs.120.25 (b) Rs.142.23 (c) Rs.112.97 (d) Rs.149.05 (e) Rs.136.50.
(1 mark)
< Answer >
57. Which of the following is not true for decision-making under conditions of risk?
(a) All the possible outcomes are known with certainty
(b) The determination of conditional profit is one of the examples of decision-making under conditions or risk
(c) Regret criterion is one of the approaches of decision-making under risk
(d) The probability assigned to each of the alternatives may be subjective or objective
(e) The decision-making has sufficient knowledge to assign probabilities to all the alternatives.
(1 mark)
< Answer >
58. A 90 percent confidence interval for population mean is (10.5, 15.5). Which of the following statement(s) is/are most
reasonable?
I. The population mean is likely to be more than 16.
II. The population mean is likely to be less than 10.
III. The population mean is likely to be less than 16.
IV. The population mean is likely to be more than 10.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Only (IV) above
(e) Both (III) and (IV) above.
(1 mark)
< Answer >
10
59. The Traffic Police Department of Kolkata has gathered data on the number of traffic accidents and number of cricket
matches that occur in the city over a weekend. According to them, there is a close relationship between the number of
accidents and the number of cricket matches played during weekends.
Number of cricket matches 18 28 8 10 13 23 32
Number of accidents 5 8 3 4 6 7 8
Assuming that there is a linear relation between these two variables, what would be your prediction about the number
of accidents that will occur on a weekend during which 25 cricket matches take place in Kolkata?
(a) 6.13 (b) 7.08 (c) 8.07 (d) 9.45 (e) 10.52.
(2 marks)
< Answer >
60. Which criterion of decision-making is not applicable when the decision maker has insufficient information to assign
any probabilities of occurrence to the various states of nature?
(a) Maximax criterion (b) Maximin criterion
(c) Hurwicz criterion (d) Regret criterion
(e) Expected value criterion.
(1 mark)
< Answer >
61. In business research, experiments are conducted for studying the cause-and-effect relationships which analyzes
(a) The changes in one variable by manipulating another variable
(b) The future sales of the product
(c) The estimate of the present value of the demand of the product
(d) The researchers to minimize the any potential errors that may crop up during the main study
(e) To develop a sampling procedure pertaining to the planning phase of the business research.
(1 mark)
< Answer >
62. The interpretation of the data that has been collected by using different analytical techniques according to the
requirements of the management is called
(a) Operational Research (b) Business Research
(c) Motivational Research (d) Analysis
(e) Market Research.
(1 mark)
< Answer >
63. Which research is used to understand the consumer behavior and also the employee behavior?
(a) Motivational Research (b) Business Research
(c) Operational Research (d) Applied Research
(e) Market Research.
(1 mark)
< Answer >
64. The term qualitative research can be criticized because:
I. It simplifies the differences between quantitative and qualitative research strategies.
II. It can only be defined in terms of what quantitative research is not.
III It does not acknowledge the variety of forms that the research strategy can assume.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Both (I) and (II) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
11
65. What is the difference between the way quantitative and qualitative researchers use existing theory?
(a) Quantitative researchers identify theories to be tested in advance, whereas for qualitative researchers theories are
drawn from analyzing the data
(b) Quantitative researchers have a limited number of relevant theories, whereas qualitative researchers have an
unlimited pool of theories to draw from
(c) Quantitative researchers are unsure of how to test for specific theories, whereas qualitative researchers follow
strict guidelines when conducting analysis
(d) Quantitative researchers are unsure of how to test conducting analysis, whereas qualitative researchers follow
strict guidelines when testing for specific theories
(e) Both (b) and (c) above.
(1 mark)
< Answer >
66. What is the problem with using strict definitions of important concepts?
(a) They prevent research from being truly objective
(b) They take the focus away from accurate measurement
(c) They prevent the researcher from assessing alternative ways of viewing a concept
(d) They prevent a consistent approach being achieved with business research
(e) In order to highlight the importance of operations management.
(1 mark)
< Answer >
67. Why do qualitative researchers place an emphasis on process?
(a) In order to demonstrate how events and patterns unfold over time
(b) To be able to establish universal causality
(c) To isolate which specific events are independent of all others
(d) In order to highlight the importance of operations management
(e) They prevent a consistent approach being achieved with business research.
(1 mark)
< Answer >
68. How might a qualitative researcher respond to the criticism that their research into IT workers cannot be generalized
to other settings?
(a) I made every effort to ensure that my respondents were representative
(b) I think that IT workers are the same regardless of where they work
(c) My research generalizes to theories not populations
(d) May be your right, I'll need to survey all IT workers right away
(e) I think that IT workers are posing towards only population surveys.
(1 mark)
< Answer >
69. In SPSS, what is the 'Data Viewer'?
(a) A table summarizing the frequencies of data for one variable
(b) A spreadsheet into which data can be entered
(c) A dialog box that allows you to choose a statistical test
(d) A screen in which variables can be defined and labeled
(e) A table where output can be saved.
(1 mark)
< Answer >
70. How is a variable name different from a variable label?
(a) It is shorter and less detailed
(b) It is longer and more detailed
(c) It is abstract and unspecific
(d) It refers to codes rather than variables
(e) Both (c) and (d) above.
(1 mark)
< Answer >
12
71. How would you use the drop-down menus in SPSS to generate a frequency table?
(a) Open the Output Viewer and click: Save As → Pie Chart
(b) Click on: Analyze → Descriptive Statistics → Frequencies
(c) Click on: Graphs → Frequencies → Pearson
(d) Open the Variable Viewer and recode the value labels
(e) Open the data viewer and click: Graphs – Frequencies.
(1 mark)
< Answer >
72. When cross-tabulating two variables it is conventional to:
(a) Represent the independent variable in rows and the dependent variable in columns
(b) Assign both the dependent and independent variables to columns
(c) Represent the dependent variable in rows and the independent variable in columns
(d) Assign both the dependent and the independent variables to rows
(e) Represent only the independent variable in column.
(1 mark)
< Answer >
73. What is a sampling frame?
(a) The report of a pilot study
(b) The selection of specific individuals to participate in the research
(c) A summary of the research process
(d) The listing of all units in the population from which the sample will be selected
(e) The samples that are collected from the population.
(1 mark)
< Answer >
74. If a researcher wishes to obtain a nationally representative sample of trade union members but does not have the
resources to travel long distances what method of sampling could they use?
(a) Stratified random sampling (b) Multi-stage cluster sampling
(c) Simple random sampling (d) Snowball sampling
(e) Cluster sampling.
(1 mark)
< Answer >
75. Quota sampling is used intensively in which type of research?
(a) Market research (b) Experimental research
(c) Action research (d) Ethnographic research
(e) Business research.
(1 mark)
< Answer >
76. What according to Quota sampling is best suitable from the following statements?
(a) The process of grouping members of the population into relatively homogeneous subgroups before sampling
(b) The process, which involves the selection of units from a list using a skip interval
(c) The process of selection of units from the population based on their easy availability and accessibility to the
researcher
(d) The process in the entire population is segmented into mutually exclusive groups or categories
(e) The process involved in selection the additional respondents based on the referrals of initial respondents.
(1 mark)
< Answer >
77. Which of the following is not the part of operational sampling process?
(a) Specifying the sample plan (b) Defining the target sample
(c) Determination of sample size (d) Specifying the sampling frame
(e) Executing the sampling plan.
(1 mark)
< Answer >
13
78. Which of the following is best suitable for ‘Random sampling error’?
(a) Occurs in collecting the data through sample surveys
(b) This is the difference between the sample results and the results of the census conducted by identical procedures
(c) Occurs only when the data is collected from the whole population
(d) Occurs when the data is not collected from the element actually selected into the sample
(e) This is the difference between the population results and the results of the multi-client surveys.
(1 mark)
< Answer >
79. Which of the following is/are the important factor(s) of a good research design?
I. The availability of adequate and skilled manpower.
II. The process of obtaining information.
III. Identifying the exact research problem to be studied.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Both (II) and (III) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
80. Among the following statements Deductive research is where:
I. The researcher uses an existing theory to develop a hypothesis.
II. The researcher subjects a hypothesis to empirical scrutiny.
III. The researcher has to transform concepts within a hypothesis into researchable entities.
(a) Only (I) above (b) Only (II) above
(c) Both (I) and (II) above (d) Both (II) and (III) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
81. From the following statements Quantitative research is:
I. More likely to take a deductive approach.
II. More likely to take an objectivist ontological position.
III. More likely to be informed by a positivist epistemological position.
(a) Only (I) above (b) Only (II) above
(c) Both (I) and (II) above (d) Both (II) and (III) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
82. Which of the following is correct under Qualitative research:
(a) It cannot be combined with quantitative research
(b) Aimed at entirely different phenomena that quantitative research is
(c) Is always inductive, interpretivist and constructivist
(d) It can serve as a prelude to quantitative research
(e) It does not expose the human perspective behind the findings.
(1 mark)
< Answer >
83 Which of the following is/are the preliminary decision(s) of a questionnaire design?
I. Required information.
II. Target respondents.
III. Interviewing technique.
(a) Only (I) above (b) Only (II) above
(c) Only (III) above (d) Both (I) and (II) above
(e) All (I), (II) and (III) above.
(1 mark)
< Answer >
14
84. The statistical difference in results between a survey that includes only those who responded and a perfect survey that
also include those who failed to respond is
(a) Response error (b) Non-response error
(c) Data processing error (d) Sample frame error
(e) Systematic error.
(1 mark)
< Answer >
85. The sampling frame error is said to occur
(a) When the list of members corresponds exactly with the target population
(b) When the list of members does not correspond exactly with the target population
(c) When the sample size does not correspond exactly with the target sample
(d) When the sample size correspond exactly with the target population
(e) When the list of members does not correspond exactly with the target sample.
(1 mark)
< Answer >
15
Suggested Answers
Quantitative Methods-II (MB152): April 2006
1.
Answer : (a)
Reason : Here, n = 3
success: family has male child
p=1/2 implies q = 1–1/2 = 1/2
so the required probability = P(0) = C(3,0)p0q3–0 =
3 1 1
1 1
2 8
× ⎛ ⎞ =
⎜ ⎟
⎝ ⎠ .
< TOP >
2. Answer : (b)
Reason : There are 13 coins in his pocket and 2 coins are drawn from it. The total no. of possible ways in which 2
coins are drawn at random is
13
2 C
If E is the event of boy’s drawing maximum amount, then n(E) =
5
2 C ( that is the boy has drawn 2 fifty
paise coins to get maximum amount)
5
2
13
2
C
P(E) 0.128
C
= =
< TOP >
3. Answer : (b)
Reason : The number of promoted persons who are men follows hypergeometric distribution.
Given details are:
N = no. of persons working in Maruti udyog = 20 .
r = no. of women candidates (labeled as success) = 9
x = desired success = 4
n = no. of promoted persons = no. of trials = 7
r (Nr) 9 (209) 11
x (n x) 4 (7 4) 3
N 20 20
n 7 7
126
P(x 4)
c c c c c
c c c
− −
− − ×
= = = = =
0.2682.
< TOP >
4. Answer : (d)
Reason : Let A be the event of drawing a red card from the first pack and B be the event of drawing a black card
from the second pack.
Since A and B are independent, in a pack there are 26 red and 26 black cards,
So, n(A)=
26
1
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 26 and n(B) =
26
1
⎛ ⎞
⎜ ⎟
⎝ ⎠ = 26
Now P(A)=
n(A)
n(S) =
26
52 =
1
2 and
P(B)=
n(B)
n(S) =
26
52 =
1
2 .
Since A and B are independent, required probability is
= P(A∩B)=P(A).P(B) =
1 . 1 1
2 2 4
=
< TOP >
16
5. Answer : (e)
Reason : Here, the total number of outcomes is 6 × 6 × 6 = 216. A sum total of 12 may appear in the following
ways: (6,1,5); (6,2,4); (6,3,3); (5,2,5); (5,3,4); (4,4,4). The first two outcomes may occur in 3! Ways = 6
ways each. The second two sets of numbers may appear in
3!
2!×1! ways = 3 ways each. While the fifth set
of numbers may appear by 3! Ways = 6 ways and the last one may come by only one ways. Hence, the
total number of outcomes that are favorable is 6×2 + 3×2 +6 + 1 = 25 ways. Hence, the required
probability will be:
25
216 .
< TOP >
6. Answer : (c)
Reason : When the population is normally distributed and the population variance is not known the t
distribution is the most appropriate for making an interval estimate with degrees of freedom = n –
1 = 5. (where n is the no.of observations).
< TOP >
7. Answer : (c)
Reason : Let X represents the number of copies of a textbook required on any day. Then X represents a binomial
distribution.
Mean (μ) = n p = 600 × 0.05 = 30 copies.
< TOP >
8. Answer : (b)
Reason : This event is called a certain event. Since the total of the numbers on the two dice certainly ranges from 2
to 12, the required probability is 1.
< TOP >
9. Answer : (c)
Reason : Here p = 1/400, probability of a defective item which is very low.
n = 100, number of items packed in the box which is quite large
The no. of defectives in a box will follow a binomial distribution
n 100, p 1
400
⎛ = = ⎞ ⎜ ⎟
⎝ ⎠
∴ μ = n p = 100 /400 = 0.25; average number of defectives in a box of 100 items.
Poison distribution with λ = μ = 0.25 can be used to find out the required probability
Probability of no defective = P(X = 0) = e−λ = e−0.25 = 0.7788.
< TOP >
10. Answer: (b)
Reason: m = n p = 10 × 0.002 = 0.02
0.02 (0.02)2 [ 2]
2!
0.9802 0.004 0.000196
2
−
= =
×
= =
P X e
Therefore, the total number of packets having two defective blades in a consignment of 10,000 packets is
= 10,000 × 0.000196 = 1.96 ≈ 2.
< TOP >
11. Answer : (c)
Reason : The graph of continuous uniform distribution is flat. The other distributions have a peak.
< TOP >
12. Answer : (d)
Reason : Given that (n p) = 20 and (n p q) = 16
∴(20. q) =16 or q = 16/20 = 0.8;
∴ p = 0.2
Now, n × 0.8 × 0.2 = 16, ∴ n =100.
< TOP >
17
13. Answer : (c)
Reason : For 25 trials the standard deviation of Z, σ = n.p.q = 6
For 25 trials V(Z) = σ2 = n.p.q = 6
or 25 p q = 6
or p q = 6 = 0.24
25
For 75 trials V(Z) = n.p.q = 75 p q
= 75 0.24
=
∴
× ×
×
∴ × ×
×
18
For 75 trials standard deviation of Z = Z = 18
= 3 2
∴
< TOP >
14. Answer : (a)
Reason : The probability that a continuous random variable will assume a particular value is zero.
< TOP >
15. Answer : (c)
Reason : The number of defective pens out of the pens randomly picked from the box follows a hypergeometric
distribution because the population of ballpoint pens is finite and it contains a specific number of
successes (defective pens).
< TOP >
16. Answer : (e)
Reason : a. The data may follow a binomial distribution if the probability of success is constant from trial to trial.
b. The data may follow a uniform distribution if the probabilities of the outcomes of the trial are equal.
c. The data may follow a normal distribution if the probability of success is constant from trial to trial.
d. The data may follow a continuous distribution if the outcome is any value within a given range of
values.
e. When sampling is done without replacement from an finite population such that the probability of
success is not constant from trial to trial, the data follow a hypergeometric distribution.
< TOP >
17. Answer : (c)
Reason : The concept of sampling distribution applies to any probability distribution from which random samples
are obtained.
< TOP >
18. Answer : (b)
Reason : The expected value of sampling distribution of mean = Population mean = 12.
< TOP >
19. Answer : (a)
Reason : E(x) = μ = 25%
x σ = n
σ
=
4
100 = 0.40%
The shape of the distribution of sample means is approximately normal. (a) is incorrect because x σ ≠
4.0%.
< TOP >
20. Answer : (e)
Reason : If we consider the process of selecting a simple random sample as an experiment then Sample mean,
Sample standard deviation, Sample range and Sample median all will be random variables because each
sample is likely to yield different values of these statistics.
< TOP >
21. Answer : (c)
Reason : When estimating population mean from a sample taken from a normal population with unknown variance
the t distribution may be used with number of degrees of freedom equal to sample size – 1.
a, b, d & e. represent incorrect degrees of freedom for using the t distribution
< TOP >
18
22. Answer : (c)
Reason : If the population is normally distributed then for any given sample size, the sampling distribution of
x
s
n
− μ
is a t distribution irrespective of the sample size being large or small.
< TOP >
23. Answer : (c)
Reason : Since the population is normal and the population variance is known the sampling distribution will be
normal with a known standard error. So the appropriate test statistic is the z statistic, which follows the
standard normal distribution.
z statistic =
2
X
x x 16 15
1.00
16
n 16
− μ − μ −
= = =
σ σ
< TOP >
24. Answer : (e)
Reason : The sample mean is used when the test involves the population mean. The difference between two sample
means is used when the test involves the difference between two population means. The sample proportion
is used when the test is about the population proportion.
< TOP >
25. Answer : (b)
Reason : p σ =
( ) 0 0 p 1 p
n
−
= 0.03098
or
0.60(1 0.60)
n
−
= 0.03098
or n = ( )2
0.60 0.40
0.03098
×
= 250.
< TOP >
26. Answer : (b)
Reason : By sampling with replacement binomial trials can be performed on a finite population with specific
number of successes and failures.
< TOP >
27. Answer : (a)
Reason : Estimated standard error of mean =
Sample standard deviation
n
Sample standard deviation,
x2 nx2 s
n 1 n 1
= −
− −
Σ
x 160 x 10
n 16
= = = Σ
∴ s =
( )2 1840 16 10 4
15 15
− =
∴ Estimated standard error of mean =
4 4 1
16 4
= =
.
< TOP >
28. Answer : (d)
Reason : In systematic sampling the first item to be included in the sample is randomly selected from the population
and the remaining items are selected at a uniform interval that is measured in time or space. The procedure
involved in cluster sampling and stratified is different from this.
< TOP >
19
29. Answer : (c)
Reason : The standard error of mean will increase if sample size is reduced.
x n
σ
σ =
If ‘n’ is reduced then σx will increase
< TOP >
30. Answer : (c)
Reason : H0 : μ = 9
H1 : μ ≠ 9
The sample is small. However since the population is normally distributed and the population variance is
known
Hence we should use the normal distribution.
x σ = n
σ
=
256
25 =3.20
z = x
x − μ
σ =
15 9
3.20
−
=1.875
At α = 0.05, the critical values are ±1.96.
The test statistic is less than the right tail critical value. So it falls in the acceptance region.
∴ We accept H0. The true mean is 9. So the test does not lead to either type I or type II error.
< TOP >
31. Answer : (a)
Reason : In testing the difference between the means of two normally distributed populations with equal and
unknown variances using small, independent random samples the correct test statistic to use is t statistic.
< TOP >
32. Answer : (b)
Reason :
( ) ( ) ( )
1 2
1 2 1 2 1 2
x x
320 144
x x 64 36 Value of the test statistic =
2.825 −
⎛ ⎞
⎜ ⎟
⎝ ⎠
− − μ −μ − − μ −μ
=
σ
( )
( ) ( )
1 2
1 2
1
0.70796
2.825
or 1 2.825 0.70796 0.999987 1
− μ −μ
= =
μ − μ = − × = − ≈ −
< TOP >
33. Answer : (c)
Reason : a. If the standard error of estimate for a regression equation is zero, then it does not indicate that the
standard deviation of the observed values of the dependent variable is zero.
b. If the standard error of estimate for a regression equation is zero, then it does not indicate that the
standard deviation of the independent variable is zero.
c. If the standard error of estimate for a regression equation is zero, then it indicates that the observed
value of the dependent variable will always be equal to its estimated value, for a given value of the
independent variable.
d. If the standard error of estimate for a regression equation is zero, then it indicates that there is a
perfect correlation between the variables.
e. If the standard error of estimate for a regression equation is zero, then it indicates that there is a
perfect correlation between the variables; so the correlation coefficient will be either –1 or 1.
< TOP >
34. Answer : (a)
Reason : The standard deviation of the sampling distribution of the mean is also called the standard error of the
mean.
< TOP >
20
35. Answer : (d)
Reason : Test statistic = x
x − μ
σ
or 1.60 =
48
5
− μ
or μ = 48 – (1.6 × 5) = 40
< TOP >
36. Answer : (b)
Reason : The confidence interval is =
x z
n
⎛ σ ⎞
± ⎜ ⎟
⎝ ⎠
Here it is given alpha equals 0.05, we need to calculate the area under the standard normal curve that
equals (1 - α ), or 95 percent. This value is ± 1.96. The confidence interval is therefore:
( )
x 1.96
n
68 1.96 2
30
68 .7156
67.2843, 68.7156
⎛ σ ⎞
± ⎜ ⎟
⎝ ⎠
⎛ ⎞
= ± ⎜ ⎟
⎝ ⎠
= ±
=
therefore (b) is the correct answer.
< TOP >
37. Answer : (c)
Reason : The standard deviation of the sampling distribution of mean depends on the sample size because it is equal
to n
σ
.
< TOP >
38. Answer : (d)
Reason :
( ) 1 2
2 2 2 2 2 1 2 2
x x
1 2
256 8
− n n 64 36
σ σ σ
σ = + = + =
22
22
2
or 256 8
64 36
or = 8 - 256 36 144
64
144 12
σ
+ =
σ ⎛ ⎞× = ⎜ ⎟
⎝ ⎠
∴ σ = =
< TOP >
39. Answer : (b)
Reason : In hypothesis testing, if the level of significance is made smaller, the rejection region becomes smaller.
< TOP >
21
40. Answer : (a)
Reason : Let the following notations be used:
X : Amount of advances (Rs. in crores)
Y : Profit after tax (Rs. in lakhs)
Coefficient of correlation is given by:
r = x . y
Cov(X,Y)
σ σ =
(X X)2 . (Y Y)2
(X X) (Y Y)
Σ − Σ −
Σ − −
A. X 7.0 5.5 5.0 4.5 4.0 4.0 ΣX=30
B. Y 54 48 42 27 19 14 ΣY=204
C. (X – X ) 2 0.5 0 –0.5 –1 –1
D. (Y – Y ) 20 14 8 –7 –15 –20
E. (X – X )2 4 0.25 0 0.25 1 1 Σ(X−X)2 = 6.5
F. (Y – Y )2 400 196 64 49 225 400 Σ(Y−Y)2 = 1334
G. (X – X )(Y – Y ) 40 7 0 3.5 15 20 Σ (X – X )(Y – Y )
= 85.5
X = n
ΣX
= 6
30
= 5.0
Y = n
ΣY
= 6
204
= 34
∴ r = 6.5 1334
85.5
× = 0.9182
Proportion of variations in profit after tax that is explained by the variations in the amount of advances =
r2 = (0.9182)2 = 0.8431
∴ Percentage of variations in profit after tax that is explained by the variations in the amount of
advances = 0.8431 × 100 = 84.31%.
< TOP >
41. Answer : (a)
Reason : If a hypothesis is tested at a 10% significance level then, it means that there is a 10% probability that
the null hypothesis will be rejected though it is true.
b, c, d & e are incorrect interpretations of the significance level
< TOP >
42. Answer : (b)
Reason : Slope of a regression equation, b =
( )
2
x
Cov X,Y
σ
=
x y
2
x
r σ σ
σ
=
0.80 5 8 1.28
25
× ×
=
< TOP >
22
43. Answer : (c)
Reason : A simple regression equation is of the form:
Yˆ = a + bX
Given:
If X = 5, ˆY =31 ∴ 31 = a + 5b………(A)
If X = 10, ˆY =47 ∴47 = a + 10b ……..(B)
Subtracting (A) from (B) we get:
47 – 31 = (10 – 5)b
16 = 5b
or b =
16 3.2
5
=
Putting the values of b in (B):
47 = a + 10 × 3.2 = a + 32
or a = 47 – 32 = 15
∴ ˆY =15 + 3.2X
Now, a =
X
Y bX Y b
n
⎛ ⎞
− = − ⎜⎜ ⎟⎟
⎝ ⎠
Σ
∴
X 60 Y a b 15 3.2 47
n 6
⎛ ⎞ ⎛ ⎞ = + ⎜⎜ ⎟⎟ = + ⎜ ⎟ = ⎝ ⎠ ⎝ ⎠
Σ
∴Mean of the observed values of Y, i.e. Y = 47
< TOP >
44. Answer : (c)
Reason : Any multiple regression equation consists of only one dependent variable and more than one
independent variables.
< TOP >
45. Answer : (a)
Reason : The covariance of a random variable with itself is always a positive quantity because it is equal to the
variance of the random variable which is always positive.
< TOP >
46. Answer : (c)
Reason : Given that,
4X,5Y X,Y
X Y X Y
Y
Y
Y
2
Y
0.80
0.80 Cov(X,Y) Cov(X,Y)
. .
or, 0.80 20
5
or, 20 5
5 0.80
5
25.
ρ =ρ =
∴ = =
σ σ σ σ
=
σ
σ = =
×
∴σ =
∴σ =
< TOP >
23
47. Answer : (b)
Reason : CV (5X) =
5X
5X
100
σ
×
μ =
X
X
5
100
5
σ
×
μ =
X
X
100
σ
×
μ
= CV (X) = 20%
Similarly CV(Y) = CV(4Y) = 40%
CV =
100
σ
×
μ or
CV
100
× μ
σ =
∴ X σ =
20 30
100
×
= 6
Y σ =
40 50
100
×
= 20
∴ X,Y
90
6 20
ρ =
× = 0.75.
< TOP >
48. Answer : (d)
Reason : (a) This is a wrong answer. If the covariance of two random variables X and Y is equal to zero then it
can be said that the random variables are independent of each other. If the variables are dependent on
each other then the covariance will assume any non-zero value.
(b) This is a wrong answer. If the coefficient of correlation is positive then we say that there is a positive
correlation between two variables.
(c) This is a wrong answer. If the coefficient of correlation is negative then we say that there is a
negative correlation between two variables.
(d) This is the correct answer. If the covariance of two random variables X and Y is equal to zero then it
can be said that the random variables are independent of each other.
(e) This is a wrong answer. If the covariance of the two random variables is zero it does not mean that
the variances of the individual variables will be zero.
< TOP >
49. Answer : (c)
Reason :
U,V
Cov(U, V)
r =
V(U)×V(V)
X,Y
Cov(2X + 10, 5Y - 7)
=
V(2X + 10)×V(5Y - 7)
2 5Cov(X, Y)
=
4V(X)×25V(Y)
10 Cov(X, Y)
=
2 5 V(X)×V(Y)
= r = 0.70
×
×
×
Covariance and variance are independent of change of origin
but dependent on change of scale.
< TOP >
50. Answer : (b)
Reason : X2 =
Σ −
e
2
o e
f
(f f )
, so, the main reason of X2 being positive is that numerator is always positive.
< TOP >
24
51. Answer : (b)
Reason : Coefficient of determination, r2 = 1–
( )
( )
2
2
Y Yˆ
Y Y
Σ −
Σ −
Y denotes the observed values and ˆY denotes the estimated values.
Y Y 792
n 8
Σ
= =
= 99
Σ(Y − Y)2 = ΣY2 − nY2 = 79144 – 8 × 992 = 736
∴ Coefficient of determination, r2 =
1 200
736
−
= 0.7283.
< TOP >
52. Answer : (d)
Reason : If the slope of a regression equation is positive, then the coefficient of correlation between the variables
involved is positive; if the slope is negative then, the there is an indirect relationship between the
variables. If the coefficient of correlation is close to zero, then there is very weak correlation between the
two variables. Correlation analysis, and not regression analysis helps in finding out how well an estimating
equation describes the relationship between the two variables. So, the option (d) is correct.
< TOP >
53. Answer : (b)
Reason : Maximize return criteria is not applicable to decision-making under risk.
Therefore (b) is the correct answer.
< TOP >
54. Answer : (e)
Reason : I. The decrease in the conditional profit when the stocked unit is not sold is called as marginal loss.
II. According to marginal analysis, the vendor should stock additional units until marginal profit is just
equal to marginal loss.
III. In decision making under uncertainty, a decision maker has insufficient information to assign a
probability.
Therefore (e) is the correct answer.
< TOP >
55. Answer : (d)
Reason : In decision-tree model, when the result of taking a decision is uncertain, then the result is represented by a
circle.
< TOP >
56. Answer : (d)
Reason :
Demand Conditional
profit under
certainty (A)
Probability of
demand (B)
Expected
profit(A x B)
28 5 x 28 = 140 0.29 40.6
30 5 x 30 = 150 0.32 48.0
31 5 x 31 = 155 0.39 60.45
149.05
The expected profit with certainty for the given situation is Rs.149.05. Therefore (d) is the correct answer
< TOP >
57. Answer : (c)
Reason : Regret criteria is used only under the conditions of uncertainty. Therefore (c) is the correct answer.
< TOP >
58. Answer : (e)
Reason : Since the 90 percent confidence interval is (10.5, 15.5) the population mean is likely to be more than
10 and less than 16.
< TOP >
25
59. Answer : (b)
Reason : Let X be the number of cricket matches played and Y be the number of accidents during weekends.
ΣX = 132, ΣY= 41, n = 7
ΣXY = 873,
ΣX2 = 2994,
X = 18.86 , Y = 5.86
The coefficient of regression b = 2 ( )2
n XY X Y
n X X
Σ −Σ Σ
Σ − Σ =
( ) ( )
( ) ( 2 )
7 873 132 41
7 2994 132
× − ×
× −
=
699
3534 = 0.198
The Y intercept a = Y − b X = 5.86 – (0.198 × 18.86) = 2.126
Therefore the estimating equation is ˆY = 2.126 + 0.198 X
The estimate of Y for X = 25, is ˆY = 2.126 + 0.198 × 25 = 7.08 (Approx)
< TOP >
60. Answer : (e)
Reason : When the decision maker has insufficient information to assign any probabilities of occurrence to the
various states of nature expected value criterion will not be applicable.
< TOP >
61. Answer : (a)
Reason : Analyzing the changes in one variable by manipulating the another variable, helps one to
identify the cause and effect relationship.
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62. Answer : (d)
Reason : The interpretation of the data that has been collected by using different analytical techniques
according to the requirements of the management is called the analysis.
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63. Answer : (a)
Reason : Motivational research involves analyzing the reasons and motives behind people’s behavior. It is
also used to understand consumer and employee behavior.
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64. Answer : (e)
Reason : Despite these criticisms qualitative research can still be a useful category, which allows for an
understanding of what is common amongst a diverse range of methods that the term encompasses.
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65. Answer : (a)
Reason : Quantitative researchers identify theories to be tested in advance, whereas for qualitative researchers
theories are drawn from analyzing the data. It is important to stress that, broadly speaking, quantitative
research employs a deductive use of theory, whereas qualitative research is generally inductive.
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66. Answer : (c)
Reason : They prevent the researcher from assessing alternative ways of viewing a concept
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67. Answer : (a)
Reason : In order to demonstrate how events and patterns unfold over time.
Most qualitative researchers view social life as a stream of interdependent events. This leads them to focus
on process as a way of uncovering how different events are linked together over time.
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68. Answer : (c)
Reason : 'My research generalizes to theories not populations.'
One of the criticisms of qualitative research is that it cannot be generalized to other contexts. A response to
this is to argue that this is not the intention of qualitative research which aims instead to seen how findings
relate to existing theories.
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69. Answer : (b)
Reason : A spreadsheet into which data can be entered.
The Data Viewer is one of the two screens that compromise the Data Editor in SPSS, the other being the
Variable Viewer. The Data Viewer is a spreadsheet grid into which you can enter your data for analysis.
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70. Answer : (a)
Reason : It is shorter and less detailed.
A variable name will appear in column or row headings and so can only be up to eight characters long. A
variable label provides a more detailed description of what this means and serves as a memo to oneself: for
example, reasons for visiting gym.
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71. Answer : (b)
Reason : Click on: Analyze → Descriptive Statistics → Frequencies.
Following this set of steps will open the 'Frequencies' dialog box in which you can select the variables you
want to analyze and then click 'ok'.
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72. Answer : (c)
Reason : Represent the dependent variable in rows and the independent variable in columns.
It is conventional to represent an inferred relationship between two variables in this way because it makes
tables easier to read. Similarly, when producing a bar chart or scatter plot, you should assign the IV to the
x axis (to produce columns) and the DV to the y axis (to produce horizontal readings).
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73. Answer : (d)
Reason : The listing of all units in the population from which the sample will be selected.
It is important to identify a sampling frame so that a representative sample can then be taken from within a
specified unit.
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74. Answer : (b)
Reason : Multi-stage cluster sampling is the correct sampling to use.
Multi-stage cluster sampling allows interviewers to concentrate their research more than simple random or
stratified sampling.
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75. Answer : (a)
Reason : Quota sampling is used intensively in Market research.
Commercial research and political opinion polling are other types of research that use quota sampling.
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76. Answer : (d)
Reason : In quota sampling, the entire population is segmented into mutually exclusive groups or categories.
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77. Answer : (b)
Reason : The options (a), (c), (d) and (e) are some of the steps involved in the operational sampling. So the option
(b) is incorrect.
It defines the target population but not the target sample.
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78. Answer : (b)
Reason : Random sampling error is denoted as the difference between the sample results and the results of the
census conducted by identical procedures.
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79. Answer : (e)
Reason : All the options of I, II and III comes under some of the important factors of good research design. So, the
option (e) is correct.
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80. Answer : (e)
Reason : All the statements I, II and III are correct. So the option (e) is the answer.
Deductive research uses theory to make observations and generate findings. Inductive research develops
theory after having made observations and generated findings.
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81. Answer : (e)
Reason : Quantitative research emphasizes quantification in the collection and analysis of data and is therefore more
likely to be characterized by the ontology of objectivism, the epistemology of positivism and a deductive
approach to theory building.
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82. Answer : (d)
Reason : Qualitative research can serve as a prelude to quantitative research in increasing the value of subsequent
quantitative research. Also helps the researcher in including the most relevant responses.
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83. Answer : (e)
Reason : All these are the preliminary decisions that are to be covered under a questionnaire design. So the option
(e) is correct.
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84. Answer : (b)
Reason : The statistical difference in results between a survey that includes only those who responded and a perfect
survey that also include those who failed to respond is known as non-response error.
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85. Answer : (b)
Reason : The sampling frame error is said to occur when the list of members does not correspond exactly with the
target population.