Chapter 9, Problem 2CRE

a)

To determine

The Hypothesis and define the parameter.

Explanation of Solution

Given:A significance test is performed to test the sensitivity with eye black and without eye black in athletes.

Sample size = n = 16

The differences in sensitivity with eye black minus without eye black are shown below

  

Let µ_d denote the average differences in sensitivity, with eye black minus without eye black.

The parameter of interest is the average sensitivity of eye black.

The test is performed to verify if there is increase in the average sensitivity of eye black.

  $\begin{array}{l}{H}_0:{\mu }_d=0\\ H_a:{\mu }_d>0\end{array}$

b)

To determine

The conditions to carry out a significance test..

Explanation of Solution

Concept used:The conditions to carry out a paired t test are

1. The sample has to be selected randomly.

2. There should not be any outliers.

3. The observeations are independent of one another or the sample should be at most 10% of the population.

The sample of 16 students are randomly selected.

The histogram of the given data indicate that there are no outliers as shown below

  

We know that there will be at least 160 students who are athletes. So the 10% condition is also satisfied.

Conclusion:All conditions for carrying out a significance test are satisfied.

c)

To determine

Interpretation of p value in the given context.

Explanation of Solution

Given:

The p value = 0.047

The p value of the test is 0.047, it means that at an average 4.7% of athletes differ from the athletes whose eye black does not increase the sensitivity.