Question

According to a past survey, 23% of Americans have hypertension. After a stringent regimen of diet and exercise, 75 people were then tested and 18 were found to have hypertension. Based on this sample, does diet and exercise reduce hypertension? Use a significance level of 0.05.a) yesb) no

Answer 1

Answer:No, Diet and exercise does not reduce hypertension.

Explanation:

Since we have given that

p = 0.23

n = 75

x = 18

So,
`\hat{p}=(x)/(n)=(18)/(75)=0.24`

So, hypothesis would be

`H_0:p=\hat{p}\\\\H_a:\hat{p}<p`

So, the test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.24-0.23}{\sqrt{(0.23* 0.77)/(75)}}\\\\z=(0.01)/(0.049)\\\\z=0.204`

At α = 0.05 level of significance, we get

critical value = 1.96

and 1.96>0.204.

so, we will accept the null hypothesis.

Hence, No, Diet and exercise does not reduce hypertension.