Question

Hypothesis Tests for Population Means when the Standard Deviation is Known

A national business magazine reports that the average age of retirement for women executives is 61.0. A women’s rights organization believes that this value does not accurately depict the current trend in retirement. To test this, the group polled a simple random sample of 95 recently retired women executives and found that they had a mean age of retirement of 61.5. Assuming the population standard deviation is 2.5 years, is there sufficient evidence to support the organization’s belief at the .05 level of significance?

Answer 1

Solution :

= 61.0

=61.5

= 2.5

n = 95

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 61.0

Ha :     61.0

Test statistic = z

= ( - ) / / n

= (61.5 -61.0 ) / 2.5 / 95

= 1.95

Test statistic = z = 1.95

P(z >1.95 ) = 1 - P(z < 1.95 ) = 1 -0.9744

P-value = 2 * 0.0256 =0.0512

= 0.05  

P-value >

0.0512 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that