Business Statistics and Research Methods Questions and Answers

Answer: B

Simple random sampling is not a restricted random sampling technique, so (B) is the answer. In simple random sampling every unit has an equal chance of selection and there is no restriction on the process. The other three place a restriction on the random selection: stratified sampling divides the population into strata and samples from each (option A), systematic sampling selects every kth unit after a random start (option C), and multistage sampling selects in stages, such as district, village and household (option D).

Answer: B

Classifying respondents only on the basis of gender is an application of the nominal scale, so (B) is correct. The categories, male and female, are names or labels with no order and no distance between them, and the only operation possible is counting the frequency in each. An ordinal scale (option A) ranks items, such as first, second and third. An interval scale (option C) has equal distances but no true zero, as with temperature in Celsius. A ratio scale (option D) has a true zero and equal distances, as with income or height.

Answer: B

Karl Pearson's coefficient of correlation is the square root of the product of the two regression coefficients, so (B) is correct. That is r = the square root of b_xy times b_yx, with the sign taken from the regression coefficients. Option (A) is wrong because the product of the standard deviations appears in the denominator when covariance is divided by it, so it is not r. Option (C) is wrong because covariance is only the numerator and has to be divided by the product of the standard deviations to give r. Option (D) is wrong because option (B) is a correct statement.

Answer: D

SPSS, STATA and MiniTab are all statistical software packages used for research in the social sciences, so (D), all of the above, is correct. SPSS, the Statistical Package for the Social Sciences, is widely used for survey data. STATA is used for econometrics and panel data analysis. MiniTab is used for statistical analysis and quality control. Since each of the three named options is a package of this kind, none of them can be chosen alone and the composite option is the answer.

Answer: D

The F-test is used for both of the later cases, so (D), '(B) and (C)', is correct. When more than two sample means are compared, the F-test in the analysis of variance tests the significance of their differences (option B). It is also used to compare the variances of two samples, as the ratio of the larger sample variance to the smaller (option C). Option (A), two sample means, is tested with the t-test, or with the Z-test for large samples, and so it is not an F-test case in its own right. Option (D) combines the two correct uses.

Answer: C

The test is a one tailed test, since the alternative hypothesis is that the first mean is less than the second, and the critical value of Z at the 5 per cent level of significance for a large sample is 1.645, option C. In a one tailed test the whole 5 per cent is placed in one tail of the normal distribution. The value 1.96 is the critical value for a two tailed test at 5 per cent. The value 2.32 is the one tailed value at 1 per cent, and 2.5758 is the two tailed value at 1 per cent.

Answer: B

Quota sampling is the non-random method of selecting samples. The interviewer is given a quota of persons of each type to cover and picks them by judgement or convenience, so not every unit has a known chance of being chosen. Stratified, systematic and cluster sampling are all probability methods: a stratified sample draws at random from each stratum, a systematic sample takes every kth unit after a random start, and a cluster sample draws whole groups at random. So the keyed answer is option B.

Answer: D

The coefficient of correlation is the square root of the product of the two regression coefficients, and it takes the sign of the coefficients:

\[ r = \pm \sqrt{0.8 \times 0.2} = \pm \sqrt{0.16} = \pm 0.4 \]

Both coefficients are positive, so r is +0.40, option D. The values 0.16 and -0.16 are the product itself, which is the square of r and not r. The value -0.40 has the wrong sign, since both regression coefficients are positive.

Answer: C

The coefficient of variation is a relative measure of dispersion. It is the standard deviation divided by the mean, usually shown as a percentage, so it is free of units and can compare the variability of series measured in different units or with different means. The standard deviation and the variance are absolute measures, which are in the units of the data, or its square, so they are not relative. The keyed answer is option C.

Answer: B

The correct match is (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii). Fisher is linked with index numbers (his ideal index), Karl Pearson with the correlation coefficient, Thomas Bayes with inverse probability, and Karl Gauss with the normal distribution.

The other codes switch the last pairs, for example giving the normal distribution to Bayes or inverse probability to Gauss, which does not follow the history of the topics.

Fisher's ideal index is the geometric mean of the Laspeyres and Paasche indices.