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 9.45 and the sample variance was 17.94. An independent random sample of 10 subjects was used as a control group and given a placebo prior to testing. The mean score in this control group was 15.36 and the sample variance was 27.93 Assuming that the population distributions are normal with equal​ variances, find a 90% confidence interval for the difference between the population mean scores.

The confidence interval is_______< μx − μy <________.

​(Round to two decimal places as​ needed.)

Answer 1

First Group:

n = 9

Mean = 9.45

Sample variance = 17.94

Second Group:

n = 10

Mean = 15.36

sample variance = 27.93

= 0.10

Degrees of Freedom = n1+n2-2 = 9+10-2 = 17

Critical value:

................Using ta table

Assuming that the population distributions are normal with equal​ variances

Calculation:

90% Confidence interval:

Therefore, the confidence interval is,

-9.76 < μx − μy < -2.06