Question

Adequate Preparation for Retirement. In 2018, RAND Corporation researchers found that 71% of all individuals ages 66 to 69 are adequately prepared financially for retirement. Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement.

a. Develop appropriate hypotheses such that rejection of H0 will support the con-clusion that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66–69 age group who did not complete high school than it is for the population of the 66–69 year old.
b. In a random sample of 300 people from the 66–69 age group who did not complete high school, 165 were not prepared financially for retirement. What is the p-value for your hypothesis test?
c. At a 5 .01, what is your conclusion?

Answer 1

A) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:p=0.71

Ha:p<0.71

This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.

B) Rejection Region: Based on the information provided, the significance level is α=0.01, and the critical value for a left-tailed test is zc​=−2.33.

The rejection region for this left-tailed test is R={z:z<−2.33}

Test Statistics

The z-statistic is computed as follows:

Using the P-value approach: The p-value is p=0.000, and since p=0.000<0.01, it is concluded that the null hypothesis is rejected.

C) It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p  from the 66–69 age group who did not complete high school is less than 0.71​, at the α=0.01 significance level.