Two quality control technicians measured the surface finish of a metal part, obtaining the data in the table below. Assume that the measurements are normally distributed. Q3. Two quality control technicians measured the surface finish of a metal part, obtaining the datain the table below. Assume that the measurements are normally distributed.Surface Finish Data:Technician 1 Technician 21.451.541.371.411.211.561.541.371.481.21.291.311.341.271.35(a) Test the hypothesis that the mean surface finish measurements made by the two technicians are equal.Use a 0.05, and assume equal variances.(b) What are the practical implications of the test in part (a)? Discuss what practical conclusions youwould draw if the null hypothesis were rejected.(c) Assuming that the variances are equal, construct a 95% confidence interval on the mean difference insurface-finish measurements.(d) Test the hypothesis that the variances of the measurements made by the two technicians are equal. Usea=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 measurementerror.(f) Construct a 95% confidence interval on the variance of measurement error for technician 2

Answered: Q3. Two quality control technicians…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two quality control technicians measured the surface finish of a metal part, obtaining the data in the table below. Assume that the measurements are normally distributed.

Q3. Two quality control technicians measured the surface finish of a metal part, obtaining the data
in the table below. Assume that the measurements are normally distributed.
Surface Finish Data:
Technician 1 Technician 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 a 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
a=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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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