Question

A survey of 12001200 workers indicated that approximately 573573 have invested in an individual retirement account. National data suggests that 4242​% of workers invest in individual retirement accounts. Test an appropriate hypothesis with alphaα=0.050.05 and state your conclusion.

Answer 1

We have given that n = 1200 and x = 573

So sample proportion is p^ = 573/1200 = 0.4775

Level of significance = 0.05

the null and alternative hypotheses are:

Ho: p=0.42

Ha: p ≠0.42

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

The significance level is α=0.05, and the critical value for a two-tailed test is Zc =1.96

Under Ho test z-statistic is,

Z = 4.0357

it is observed that |z| = 4.036 >zc​=1.96

So we reject the null hypothesis

We conclude that national data does not suggest that 42% of workers invest in individual retirement.