Question

When 583 female workers in the 2012 GSS were asked how many hours they worked in the previous week, the mean was 37.0 hours, with a standard deviation of 15.1 hours. Does this suggest that the population mean work week for females is significantly different from 40 hours? Answer by: (10 points)

A) Identifying the relevant variable and parameter
B) Stating the null and alternative hypotheses
C) Reporting and interpreting the p-value for the test statistic value
D) Explaining how to make a decision for the significance level of 0.01.

Answer 1

A)

We are given that:

And, we want to test whether .

B)

The null and alternate hypothesis are:

H0:

Ha:

C)

The test statistic value is given by:

Since this is a two-tailed test, so the p-value is given by:

D)

Since this p-value is less than 0.01, so we have sufficient evidence to reject the null hypothesis H0.

So, we can say that .