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Given in the question that

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

Sample size $n=16$. we have to State hypotheses, Be sure to define the parameter.

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

Let$渭d$denote the average sensitivity differential between with and without eye black.

The average sensitivity of eye black is the parameter of interest. The test is carried out to see if the average sensitivity of eye black has increased.

$H_0:渭d=0$

$H_{伪}:渭d>0$

we have to Check conditions for carrying out a significance test.

The following are the requirements for conducting a paired test: 1. A random sample must be chosen.

2. No outliers should exist.

3. The observations are unrelated to one another, or the sample is no more than $10\%$of the total population.

The students in the sample were chosen at random.

There are no outliers in the data, as seen in the histogram below:

we know that there will be at least $160$students who are athletes.so the $10\%$condition is also satisfied.

Given in the question that $Pvalue=0.047$we have to Interpret this value in context.

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.