Question

Your non-profit is competing for the expansion of a program that reviews individuals’ education and experience for assignment to an appropriate work retraining program. Previous studies have found that the average amount of time required for the initial interview for this to have a population standard deviation of 8 minutes.

You have implemented some changes in how your non-profit does this interview and you claim that at your site the amount of time needed for it is less than 50 minutes. Your boss knows that you took statistics and asks you to provide some evidence that your claim is correct. You take a sample of 25 individuals and find a mean of 45 minutes per interview. Using the technique you learned in this class test your claim at the .01 significance level. Be sure to show the claim and the null and alternative hypothesis. What do you conclude? What do you conclude about the claim?

Answer 1

Solution :

Given that ,

= 50  

= 45

= 8

n = 25

The null and alternative hypothesis is ,

H₀ :   = 50

H_a : < 50

This is the left tailed test .

Test statistic = z

= ( - ) / / n

= ( 45 - 50) / 8 / 25

= -3.125

The test statistic = -3.125

P - value = P (Z < -3.125 ) = 0.0009

P-value = 0.0009

= 0.01

0.0009 < 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to test the claim.