Question

The AARP (American Association of Retired People) report that at least 60% of retired people under the age of 65 would return to work on a full-time basis if a suitable job were available. A sample of 500 retirees under the age of 65 showed that 315 would return to work. Can we conclude that more than 60% would return to work? Test at the 2% level of significance.

Answer 1

Explanation:

Proportion of retired people under the age of 65 would return to work on a full-time basis if a suitable job were available = 60/100 = 0.6 = P

Null hypothesis: P ≤ 0.6

Alternative: P > 0.6

First, to calculate the hypothesis test, lets workout the standard deviation

SD = √[ P x ( 1 - P ) / n ]

where P = 0.6, 1 - P = 0.4, n = 500

SD = √[ (0.6 x 0.4) / 500]

SD = √ (0.24 / 500)

SD = √0.00048

SD = 0.022

To calculate for the test statistic, we have:

z = (p - P) / σ where p = 315/500 = 0.63, P = 0.6, σ = 0.022

z = (0.63 - 0.6) / 0.022

z = 0.03/0.022

z = 1.36

At the 2% level of significance, the p value is less than 98% confidence level, thus we reject the null hypothesis and conclude that more than 60% would return to work.