The recovery time (in days) is measured for 10 patients taking a new drug and for 10 different patients taking a placebo. We wish to test the hypothesis that the mean recovery time for patients taking the drug is less than for those taking placebo. The data are:

With drug: 15,10,13,7,9,8,21,9,14,8

Placebo: 15,14,12,8,14,7,16,10,15,12

A. Perform a hypothesis testing under an assumption of normality and equal population variances.

*Solution:*

Codes:

Output:

Interpretation: We lack the evidence to reject the null hypothesis with p-value at 0.3002, hence the true difference in mean recovery time for patients taking drug is either equal to or greater than those taking placebo.

B. Perform a hypothesis testing under an assumption of normality and unequal population variances.

*Solution: *

Codes: (Using the defined data above)

Output:

Interpretation: Still, we lack the evidence to reject the null hypothesis at p = 0.3006, and so the true difference in mean recovery time for patients taking the drug is either equal to or greater than those taking a placebo.

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**Tags:** Examples, R Programming, two sample t-test