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.

*Related*

To

**leave a comment** for the author, please follow the link and comment on their blog:

** ALSTAT R Blog**.

R-bloggers.com offers

**daily e-mail updates** about

R news and

tutorials on topics such as:

Data science,

Big Data, R jobs, visualization (

ggplot2,

Boxplots,

maps,

animation), programming (

RStudio,

Sweave,

LaTeX,

SQL,

Eclipse,

git,

hadoop,

Web Scraping) statistics (

regression,

PCA,

time series,

trading) and more...

If you got this far, why not

__subscribe for updates__ from the site? Choose your flavor:

e-mail,

twitter,

RSS, or

facebook...

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