A company employs two shifts of workers. Each shiftĂ‚Â produces a type of gasket where the thicknessĂ‚Â is the critical dimension. The average thickness and the standard deviation of thickness for shift 1, based on a random sample of 30 gaskets, are 10.53 mm and 0.14 mm. The similar figures for shift 2, based on a random sample of 25 gaskets, are 10.55 mm and 0.17 mm. Let ĂŽÂĽ1 Ă˘Ë†â€™ ĂŽÂĽ2 be the mean difference in thickness between shifts 1 and 2.
a. Calculate a 95% confidence interval for ĂŽÂĽ1 Ă˘Ë†â€™ ĂŽÂĽ2.
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?
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c. How would your answers to parts a and b change if the sample sizes were instead 300 and 250?