Question

A manager is looking at the number of sick days used by employees in a year.

H0: the average number is 8 or below

H1: the average is over 8

We know that the standard deviation of the number of sick days used by employees is 2, and we want to test at 10% significance level.

Say we took a random sample of 50 employees, and checked their records, and found that the average was 8.1

The manager figures that the critical value (z-sub-0.1) is 1.28.

What should be the decision?

	A.	Employees are abusing their sick days
		B. Reject H0
		C. We have insufficient information to make a decision
		D. Keep H0

Answer 1

Let the hypotheses are:

Rejection region:

Reject Ho if Z_obs>Z_0.10=1.28

Since, n=50, hence we use Z statistic here and one tail Z test to test the hypothesis

Test Statistic:

P-value:

P value associated with the calculated Z statistic is computed using the Z table shown below:

P value:0.363

Conclusion:

Since Z(obs)<Z( critical and P-value is greater than the level of significance (0.10), we fail to reject the null hypothesis, therefore we have insufficient evidence to support the claim.

D. Keep H0