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.

Step-by-step explanation:

Since we have given that

p = 0.23

n = 75

x = 18

So, $\hat{p}=\dfrac{x}{n}=\dfrac{18}{75}=0.24$

So, hypothesis would be

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

So, the test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.24-0.23}{\sqrt{\dfrac{0.23\times 0.77}{75}}}\\\\z=\dfrac{0.01}{0.049}\\\\z=0.204$

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.