Question

Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded a mean of 2.765 years and s = 0.8. Use a = 0.01. Assume normal distribution.

Answer 1

We have the sample data are as   n=64, =2.765 years and s=0.8.

• Step 1. Set up hypotheses and determine level of significance

H0: μ = 3 H1: μ < 3 α =0.01

Here left tailed test is used.

• Step 2. Select the appropriate test statistic.

Because the sample size is large (n>30) the appropriate test statistic is

• Step 3. Set up decision rule.

we are performing a left tailed test (H1: μ<3), with a Z test statistic and selected α =0.01. Reject H0 if Z < -2.33

• Step 4. Compute the test statistic.

We now substitute the sample data into the formula for the test statistic Z =

  

=- 2.35

• Step 5. Conclusion.

We reject H0 because -2.35 < - 2.33  We have statistically significant evidence at a =0.01 to show that the mean time an employee stays with a company in their current positions is less than 3 years .