Answered: a) Test the hypothesis that the mean…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 15SBE

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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 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?

- TABLE 4E.1
Surface Finish Data for Exercise 4.17
Technician 1
Technician 2
1.45
1.54
1.37
1.41
1.21
1.56
1.54
1.37
1.48
1.20
1.29
1.31
1.34
1.27
1.35

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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