9. The Taylor Steel Company wants to determine whether there is a significant difference in productivity between day-shift workers and night-shift workers. A random sample of 130 day-shift workers shows a mean output of 66.3 parts per hour with a standard deviation of 14.0 parts per hour, while a random sample of 120 night-shift workers shows a mean output of 62.7 parts per hour with a standard deviation of 16.0 parts per hour. a. Is there evidence in these results of a difference in productivity between day-shift and night- shift workers? Use a 5% significance level. (Do not assume that the two population standard deviations are equal. Show all four steps of your hypothesis test.) b. Calculate a 95% confidence interval for the difference between the group means. What does this confidence interval imply about whether you can reject the null hypothesis of no difference in productivity between the two shifts? Is this result consistent with the results of your t-test of the difference in means in part a? Explain why it is (or isn't).