Continue with the assumptions and summaries from Problem 5. Derive the 95% confidence interval for the expected difference, (D) = 1 2.

1. Show critical value (or values)

2. Indicate upper and lower confidence limits.

ASSUMPTIONS AND SUMMARIES FROM PROBLEM 5:

Payroll specialists conduct a comparative study of wages paid to full-time technicians and their colleagues working on temporary contracts.

Two samples of size n1 = n2 = 9 each were collected independently:

X1 = {X1[j] : 1 j n1 = 9} and X2 = {X2[j] : 1 j n2 = 9}

Based on the history, payroll experts assume that all records are normally distributed with unknown means,(mu1, 2), and known population standard deviations,

1 = 9 and 2 = 12,

hence corresponding variances are: (1) 2 = (9)2 = 81 and (2) 2 = (12)2 = 144 The means, 1 and 2 remain unknown. Sample summaries are presented in the form of a table below.

Group	Size	Sample Mean	Population Variance
Full Time	n1 = 9	Xbar1 = 164	(1) 2 = 81
Contractors	n2=9	Xbar2 = 175	(2) 2 = 144