Regardless of age, about 20% of American adults participate in fitness activities at least twice a week. A random sample of 100 adults over 40 years old found 15 who exercised at least twice a week. Is this evidence of a decline in participation after age 40? Use α = .05. a) Write test hypothesis b) Compute test statistic. c) Apply any method to draw conclusion.

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.

Step-by-step 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.

(8+64)^2= 5184 < answer

step-by-step explanation:

2^3 = 8

4^3= 64

(8+64)^2 = 5184