Question

Problem 1: Adults saving for retirement Please type your answer, thank you.

In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance.

1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?

Answer 1

Solution

Sample proportion is= P = 156/295 = 0.52881

State the null and alternative hypothesis.

H0:p=0.5 and H1:p>0.5

What type of hypothesis test is to be used?

parametric z-test should be used

What distribution should be used and why?

standard normal distribution

Is this a right, left, or two-tailed test?

right

Compute the test statistic.

z=(P-p)/sqrt(p(1-p)/n)=(0.5288-0.5)/sqrt(0.5*(1-0.5)/295)=0.9893

Compute the p-value.

0.16 (using P(Z>0.9893))

Do you reject or not reject the null hypothesis? Explain why.

donot reject null hypothesis H0 as p-value is more than level of significance alpha=0.05

What do you conclude?

sample evidence does not suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement