Question

Technician           Technician

A B

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

Technician           Technician

1                              2

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

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 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.Please solve urgent

Answer 1

Let here denote the mean of techniacian A

and for B then our hypothesis will be

If the observations from the populations are denoted by:

and

Then test statistic in this case is given by:

where

(Technician A)

(Technician B)

So based on the above formulas the test statistic is given by:

t = -0.019737~ t_8+7-2 ~ t₁₃

So p value is given by:

p value = P(t₁₃ > |t|) = P(t₁₃ > |-0.019737) = P(t₁₃ > 0.019737) = 0.4922764

Since p value > which implies that we do not have enough evidence to reject H0

So H0 is true which implies that mean of both technicians are same.

95% CI is given by:

After putting values we get

(-0.1399483 ,0.1374483)

critical value is calcullated in R

and code for the same is attached herewith