Question

Question:

(Need the hand-written answer, not using minitab, please)

Two quality control technicians measured the surface finish of a metal part, obtaining the data shown. Assume that the measurements are normally distributed. a) Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use α = 0.05 and assume equal variances. b) What are the practical implications of the test in part

(a)? Discuss what practical conclusions you would draw if the null hypothesis were rejected?

c) Assuming that the variances are equal. Construct a 95% confidence interval on the mean difference in the surface-finish measurements.

d) Test the hypothesis that the variances of the measurements made by the two technicians are equal. Use α = 0.05. What are the practical implications if the null hypothesis is rejected?

e) Construct a 95% confidence interval estimate of the ratio of the variances of technician measurement error. f) Construct a 95% confidence interval on the variance of measurement error for technician 2.

g) Does the normality assumption seem reasonable for the data?

Technician 1 Technician 2 1.45 1.37 1.21 1.54 1.48 1.29 1.34 1.54 1.41 1.56 1.37 1.20 1.31 1.27 1.35

Answer 1

X, 1,383 .O132 0,0156 b-8-4:1546 nne- 0:1204 0.1123 ignfi comer ゆBoth thu samf4 ah. Joum · in h =0,0여to. 158 -(-0.151,0 , les 2- 20, 013 ー ,of 56,一0.8462

Retain the null hypothesis at 0.05 level of significance.

The practical implication of the test is that both the data are drawn from normal distributions.

046 2 o, ·欠 ㅁ o '0153 <0,2/0,0 1 56 1.62 99 16.0128