Answer:
The null hypothesis is

The alternate hypothesis is

The p-value of the test is 0.1056 > 0.05, which means that there is not evidence of decline in participation after age 40 using α = 0.05.
Explanation:
20% of American adults participate in fitness activities at least twice a week. Test if there is evidence of a decline in participation after age 40.
At the null hypothesis, we test that the proportion is of 0.2, so:

At the alternate hypothesis, we test if the proportion is less than 0.2, indicating a decline. So

The test statistic is:

In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
20% is tested at the null hypothesis:
This means that

A random sample of 100 adults over 40 years old found 15 who exercised at least twice a week.
This means that

Test statistic:



P-value of the test:
The p-value of the test is the probability of finding a sample proportion below 0.15, which is the p-value of z = -1.25.
Looking at the z-table, z = -1.25 has a pvalue of 0.1056.
The p-value of the test is 0.1056 > 0.05, which means that there is not evidence of decline in participation after age 40 using α = 0.05.