Question

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 51 day-shift workers was 331. The mean number of units produced by a sample of 56 night-shift workers was 337. Assume the population standard deviation of the number of units produced on the day shift is 20 and 27 on the night shift. At the 0.10 significance level, is the number of units produced on the night shift larger?

Is this a one-tailed or a two-tailed test? One-tailed test Two-tailed test

State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

What is your decision regarding H0?

Do not reject H0.

Reject H0.

Answer 1

Let ,
11
be the population mean number of units produced by a day-shift workers and
112
be the population mean number of units produced by a night-shift workers.

1) The null and alternative hypothesis is ,

Ho: M1 = 42

$H_a:\mu_1<\mu_2$

The test is left-tailed test.

The critical value is ,

$Z_{\alpha/2}=Z_{0.10/2}=-1.64$ ; From Z-table

The decision rule is ,

Reject Ho , if Z-stat<-1.64 , otherwise do not  reject Ho.

The test statistic is ,

$Z_{stat}=\frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}=\frac{331-337}{\sqrt{\frac{20^2}{51}+\frac{27^2}{56}}}=-1.31$

Decision : Here , Z-stat=-1.31>-1.64

Therefore , do not reject Ho.

COnclsuion : There is not sufficient evidence to support the claim that there are more units produced on the night shift than on the day shift.