# Statistics MCQs – Hypothesis Testing for Two Populations Part 6

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101. A random sample is drawn from each of two normally distributed populations. The sample size for sample 1 is 16 and the sample standard deviation is 15. The sample size for sample 2 is 13 and the standard deviation is 10. We wish to test at the 10 % level of significance whether there is enough evidence to infer that the two population variances differ. What is the value of the test statistic in this case?

a. 2.36

b. 2.62

c. 2.25

d. 1.21

e. 1.86

Answer: C

102. A random sample is drawn from each of two normally distributed populations. The sample size for sample 1 is 16 and the sample standard deviation is 11. The sample size for sample 2 is 13 and the standard deviation is 10. We wish to test at the 10 % level of significance whether there is enough evidence to infer that the two population variances differ. What is the value of the test statistic in this case?

a. 2.36

b. 2.62

c. 2.25

d. 1.21

e. 1.86

Answer: D

103. A random sample is drawn from each of two normally distributed populations. The sample size for sample 1 is 16 and the sample standard deviation is 15. The sample size for sample 2 is 13 and the standard deviation is 10. We wish to test at the 10 % level of significance whether there is enough evidence to infer that the two population variances differ. What is the conclusion, based on a 10 % significance level?

a. Reject H_{0} and conclude that the two population variances differ

b. Fail to reject H_{1} and conclude that the two population variances differ

c. Fail to reject H_{0} and conclude that the two population variances do not differ

d. Fail to reject H_{0} and conclude that the two population variances differ

e. Accept H_{0} and conclude that the two population variances do not differ

Answer: C

104. A random sample is drawn from each of two normally distributed populations. The sample size for sample 1 is 16 and the sample standard deviation is 11. The sample size for sample 2 is 13 and the standard deviation is 10. We wish to test at the 10 % level of significance whether there is enough evidence to infer that the two population variances differ. What is the conclusion, based on a 10 % significance level?

a. Reject H_{0} and conclude that the two population variances differ

b. Fail to reject H_{1} and conclude that the two population variances differ

c. Fail to reject H_{0} and conclude that the two population variances do not differ

d. Fail to reject H_{0} and conclude that the two population variances differ

e. Accept H_{0} and conclude that the two population variances do not differ

Answer: C