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) are the samples paired or independent? (b) construct a 95% confidence interval for. (c) based on your answer to (b), are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? why or why not? be brief and to the point.