A researcher intends to estimate the effect of a drug on the scores of human sub

Question

A researcher intends to estimate the effect of a drug on the scores of human
subjects performing a task of psychomotor coordination. The members of a random
sample of 9 subjects were given the drug prior to testing. The mean score in this group
was 9.78, and the sample variance was 17.64. An independent random sample of 10
subjects was used as control group and given a placebo prior to testing. The mean score
in this control group was 15.10, and the sample variance was 27.01.
a. Assuming the two populations are normal, test the null hypothesis that the
population variances are equal against the alternative hypothesis that the
population variance is higher for the control group. Assume =0.05.
b. Depending on your answer to part (a) (whether the population variances can be assumed
to be equal or not), find a 90% confidence interval for the difference between the
population mean scores.

Explanation / Answer

Given : first sample-tested group , size n1 = 9; mean =9.78; variance =17.64, SD =sqrt(variance)=4.2

second sample- Control group : size n2 =10; mean =15.10; variance =27.01; SD= sqrt(27.01)=5.197

a. Null hypothesis: The population variance are equal; Alternative hypothesis: The population variance is higher for the control group.

Assuming the two populations are normal and equal variance and at =0.05.

B) the population variances are equal

a 90% confidence interval for the difference between the population mean scores is (1.52,9.12)

F Test for Differences in Two Variances Data Level of Significance 0.05 Larger-Variance Sample Sample Size 10 Sample Standard Deviation 5.197 Smaller-Variance Sample Sample Size 9 Sample Standard Deviation 4.2 Intermediate Calculations F Test Statistic 1.531112 Population 1 Sample Degrees of Freedom 9 Population 2 Sample Degrees of Freedom 8 Upper-Tail Test Upper Critical Value 3.38813 p-Value 0.279719 Do not reject the null hypothesis

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