It has been suggested that night shiftworkers show more prod

It has been suggested that night shift-workers show more productivity in their output levels than day workers. Below, you are given the results of two small independent random samples. The management would like you to conduct a hypothesis test of the differences in means between these two groups.

                                                            Night Shift     Day Shift

                        Sample Size                          9                        8

                        Sample Mean                    520                  540

                        Sample Variance                 36                    25

            a.   State the null and alternative hypotheses to be tested.

            b.   Compute the test statistic.

            c.    Determine the p-value

            d.    State your conclusion

Solution

Set up null and alternate as

H0: mu1 = mu 2

Ha: mu1 not equals mu2

As sample sizes are small t statistic is used

  The mean of Group One minus Group Two equals -20.00
  95% confidence interval of this difference: From -36.90 to -3.10

b) t = 2.5230
  df = 15
  standard error of difference = 7.927

c) The two-tailed P value equals 0.0234
d) By conventional criteria, this difference is considered to be statistically significant.

The two productivity can be taken to be equal.