Each of these problems can be solved using a confidence inte

Each of these problems can be solved using a confidence interval to test a hypothesis. Write the null and alternative hypotheses. State the significance level. Construct a confidence interval. Make your decision about the null hypothesis. Write a conclusion. Do any i of these problems. The problem is worth 25 points. According to menstuff.org, 22% of married men have \"stayed\" at least once during their married lives. A survey of 500 married men results in 122 indicating that they have \"strayed\" at least once during their married lives. Construct a 95% contidence level tor me population proportion of men who have strayed. Use it to assess the accuracy of the statement made by menstuff.org.

Solution

Null hypothesis: p=0.22

Alternative hypothesis: p not equal to 0.22

The significant level a=1-0.95=0.05

The critical value is Z(0.025) = 1.96 (from standard normal table)

p=122/500 = 0.244

The lower bound is

p - Z*sqrt(p*(1-p)/n) =0.244 -1.96*sqrt(0.244*(1-0.244)/500) =0.2063533

The upper bound is

p + Z*sqrt(p*(1-p)/n) =0.244 +1.96*sqrt(0.244*(1-0.244)/500) =0.2816467

Since the inerval includes 0.22, we do not reject the null hypothesis.

So we can conclude that 22% of married men have strayed at least once during their married lives.