A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The average thickness and the standard deviation of thickness of shift 1, based on a random sample of 30 gaskets, are 10.53mm and 0.14mm. The similar figures for shift 2, based on a random sample of 25 gaskets, are 10.55mm and 0.17mm. Let µ1-µ2 be the mean difference in thickness between shifts 1 and 2.
a) Find a 95% confidence interval for µ1-µ2.
b) Based on your answer to part a, are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? Why or why not?
c) How would your answers to parts a and b change if the sample sizes were instead 300 and 250?