It has been suggested that night shift-workers show more productivity in their o

Question

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

Explanation / Answer

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.

Group   Group One     Group Two   Mean 520.00 540.00 SD 18.00 14.14 SEM 6.00 5.00 N 9     8    

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