Question

A study was conducted by the U.S. Army to see if applying antiperspirant to soldiers' feet for a few days before a major hike would help cut down on the number of blisters soldiers had on their feet. In the experiment, for three nights before they went on a 13-mile hike, a group of 328 West Point cadets put an alcohol-based antiperspirant on their feet. A "control group" of 339 soldiers put a similar, but inactive, preparation on their feet. On the day of the hike, the temperature reached 83°F. At the end of the hike, 21% of the soldiers who had used the antiperspirant and 48% of the control group had developed foot blisters.† Conduct a hypothesis test at the 5% level to see if the percent of soldiers using the antiperspirant was significantly lower than the control group.

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A) State the distribution to use for the test. (Round your answers to four decimal places.)

P'_a−P'_na~(__,__)

B) What is the test statistic? (Round your answer to two decimal places.)

C)What is the p-value?

Please show steps using ti-84 plus.

Answer 1

Here we have

Hypotheses are:

Press stat button on calculator. You will get following screen :

Then go to test , then 2 prop z test as follows:

Click enter and enter data as follows:

Select calculate and press enter. You will get the following results:

The test statistics is :

z = -7.33

The p-value:

p-value = 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis. On the basis of sample evidence we can conclude that the percent of soldiers using the antiperspirant was significantly lower than the control group.