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4-60. Amachine produces metal rods used in an automobile suspension system. A random sample of 12 rods is selected, and the diameter is measured. The resulting data in millime- ters are shown here. 8.23 8.29 8.19 8.14 8.31 8.19 8.29 8.32 8.42 8.24 8.30 8.40 (a) Check the assumption of normality for rod diameter. (b) Is there strong evidence to indicate that mean rod diame- ter is not 8.20 mm using a fixed-level test with a = 0.05? (c) Find the P-value for this test. (d) Find a 95% two-sided CI on mean rod diameter and pro- vide a practical interpretation of this interval.

4-60. Amachine produces metal rods used in an automobile suspension system. A random sample of 12 rods is selected, and the diameter is measured. The resulting data in millime- ters are shown here. 8.23 8.29 8.19 8.14 8.31 8.19 8.29 8.32 8.42 8.24 8.30 8.40 (a) Check the assumption of normality for rod diameter. (b) Is there strong evidence to indicate that mean rod diame- ter is not 8.20 mm using a fixed-level test with a = 0.05? (c) Find the P-value for this test. (d) Find a 95% two-sided CI on mean rod diameter and pro- vide a practical interpretation of this interval.

MATLAB: An Introduction with Applications
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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Parts a-d
Title: Statistical Analysis of Rod Diameters in Automobile Suspension Systems Introduction: In the production of metal rods used in the suspension systems of automobiles, it is crucial to ensure that the diameters conform to specified measurements. A random sample of 12 rods was selected to measure their diameters, with the data recorded in millimeters as follows: Sample Data (Diameter in mm): - 8.23, 8.31, 8.42 - 8.14, 8.19, 8.19 - 8.29, 8.29, 8.24 - 8.32, 8.30, 8.40 Analysis Tasks: (a) **Check the Assumption of Normality**: Determine if the diameters of the rods follow a normal distribution, which is a key assumption for many statistical tests. (b) **Test for Mean Difference**: Investigate if there is significant evidence to suggest that the mean rod diameter differs from 8.20 mm. This is done using a fixed-level test with a significance level (\(\alpha\)) of 0.05. (c) **P-Value Calculation**: Calculate the p-value for the test conducted in part (b) to assess the strength of the evidence against the null hypothesis. (d) **Confidence Interval**: Compute a 95% two-sided confidence interval on the mean rod diameter. Provide a practical interpretation of this interval to understand the range within which the true mean diameter is likely to fall. By conducting these analyses, we can make data-driven decisions to ensure the quality and consistency of rod production in automotive suspension systems.
Transcribed Image Text:Title: Statistical Analysis of Rod Diameters in Automobile Suspension Systems Introduction: In the production of metal rods used in the suspension systems of automobiles, it is crucial to ensure that the diameters conform to specified measurements. A random sample of 12 rods was selected to measure their diameters, with the data recorded in millimeters as follows: Sample Data (Diameter in mm): - 8.23, 8.31, 8.42 - 8.14, 8.19, 8.19 - 8.29, 8.29, 8.24 - 8.32, 8.30, 8.40 Analysis Tasks: (a) **Check the Assumption of Normality**: Determine if the diameters of the rods follow a normal distribution, which is a key assumption for many statistical tests. (b) **Test for Mean Difference**: Investigate if there is significant evidence to suggest that the mean rod diameter differs from 8.20 mm. This is done using a fixed-level test with a significance level (\(\alpha\)) of 0.05. (c) **P-Value Calculation**: Calculate the p-value for the test conducted in part (b) to assess the strength of the evidence against the null hypothesis. (d) **Confidence Interval**: Compute a 95% two-sided confidence interval on the mean rod diameter. Provide a practical interpretation of this interval to understand the range within which the true mean diameter is likely to fall. By conducting these analyses, we can make data-driven decisions to ensure the quality and consistency of rod production in automotive suspension systems.
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