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 for shift 1, based on a random sample of 40 gaskets, are 10.85 mm and 0.16 mm, respectively. The similar figures for shift 2, based on a random sample of 30 gaskets, are 10.90 mm and 0.19 mm. Let be the difference in thickness between shifts 1 and 2, and assume that the population variances are equal.
-(A) Construct a 95% confidence interval for .
(B) Based on your answer to (A), are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? Why or why not?

Question

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 for shift 1, based on a random sample of 40 gaskets, are 10.85 mm and 0.16 mm, respectively. The similar figures for shift 2, based on a random sample of 30 gaskets, are 10.90 mm and 0.19 mm. Let  be the difference in thickness between shifts 1 and 2, and assume that the population variances are equal.
-(A) Construct a 95% confidence interval for  .
(B) Based on your answer to (A), are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? Why or why not?

Quizplus · Accepted Answer

The Answer of 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 for shift 1, based on a random sample of 40 gaskets, are 10.85 mm and 0.16 mm, respectively. The similar figures for shift 2, based on a random sample of 30 gaskets, are 10.90 mm and 0.19 mm. Let  be the difference in thickness between shifts 1 and 2, and assume that the population variances are equal.
-(A) Construct a 95% confidence interval for  .
(B) Based on your answer to (A), are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? Why or why not?

A Company Employs Two Shifts of Workers