Continue with the assumptions and summaries from Problem 5.

1. At the significance level, = 0.01, do you have enough evidence that average wages of full time technicians are lower than those for contractors?

2. At the significance level, = 0.05, do you have enough evidence to conclude that population average for two groups differ?

Evaluate test statistic, show critical values and state rejection rules for each case!

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