Question

New Balance, a major athletic-wear company, is dissatisfied with the number of employee days lost due to sickness. Per employee, the mean number of days lost per year is 21, and the standard deviation is 5. In order to try to reduce this loss, the board of directors appoint an occupational psychologist to make recommendations for changes in corporate policy. The psychologist suggests that providing free fitness classes at lunchtimes could help. The directors agree to try providing these classes at one corporate location. After one year, the number of days lost for each employee at the corporate location is as follows: 25, 26, 16, 15, 26, 14, 23, 4, 17, 21, 22, 5, 14, 20, 10, 18 a) Represent the null and alternative hypotheses in symbol form b) Identify the rejection region using  = 0.05 for a two-tailed test. Draw a rough graph showing the critical region. c) What conclusions can be drawn from this study about the effect of providing free fitness classes on the number of employee days lost due to sickness? Be sure to state your conclusions in plain English.

Answer 1

a)

The Null and Alternative Hypotheses are,

where is the mean number of days lost in sample

b)

Since the population standard deviation is known, the z distribution is used to test the hypothesis.

The critical value for the z is obtained from the z distribution table for significance level = 0.05 and a two-tailed hypothesis.

Hence the rejection region is,

such that reject the null hypothesis if the obtained z statistic is greater than the critical value.

c)

The z statistic is obtained using the formula,

Conclusion:

Since the z statistic is greater than 1.96 at a 5% significance level for the two-tailed hypothesis, the null hypothesis is rejected. hence we can conclude that the mean number of days lost is significantly different than 21 (significantly less than 21).

Hence providing fitness classes has a significant effect on the number of employee days lost due to sickness.