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:No, Diet and exercise does not reduce hypertension.Step-by-step explanation:Since we have given that p = 0.23n = 75x = 18So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{18}{75}=0.24[/tex]So, hypothesis would be [tex]H_0:p=\hat{p}\\\\H_a:\hat{p}<p[/tex]So, the test statistic value would be [tex]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[/tex]At α = 0.05 level of significance, we get critical value = 1.96and 1.96>0.204.so, we will accept the null hypothesis.Hence, No, Diet and exercise does not reduce hypertension.