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Question 4 (8 parts): A manufacturer's truck tire is designed to have a sidewall depth of 1.1 cm. If the sidewall is too deep, the tire will handle poorly; if the sidewall is too shallow, the tire will not be durable. Recently, customer complaints have led the manufacturer to suspect that its tires' sidewall depth may not meet the design specification u= 1.1 cm. Destructive testing is expensive, so the manufacturer has drawn a random sample of 50 tires from its production line which were cut open to measure sidewall depth. Depth measurements are recorded the Midterm Exam Workbook. a. Conduct the appropriate hypothesis test to determine whether there is strong evidence that sidewall depth is not in compliance with the manufacturer's specification. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one- tailed test to the right, or a two-tailed test? b. What is the p-value for the test statistic in (a)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). c. Based on the results from (a) and (b), what is your conclusion about the average tire sidewall depth at a = .05?

Question 4 (8 parts): A manufacturer's truck tire is designed to have a sidewall depth of 1.1 cm. If the sidewall is too deep, the tire will handle poorly; if the sidewall is too shallow, the tire will not be durable. Recently, customer complaints have led the manufacturer to suspect that its tires' sidewall depth may not meet the design specification u= 1.1 cm. Destructive testing is expensive, so the manufacturer has drawn a random sample of 50 tires from its production line which were cut open to measure sidewall depth. Depth measurements are recorded the Midterm Exam Workbook. a. Conduct the appropriate hypothesis test to determine whether there is strong evidence that sidewall depth is not in compliance with the manufacturer's specification. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one- tailed test to the right, or a two-tailed test? b. What is the p-value for the test statistic in (a)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). c. Based on the results from (a) and (b), what is your conclusion about the average tire sidewall depth at a = .05?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.4: Polyhedrons And Spheres
Problem 23E: The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each...
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Sidewall Depth (cm)
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1.06
1.16
1.11
1.06
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1.13
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1.16
1.12
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1.07
1.14
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1.17
1.11
1.16
1.18
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1.04
1.03
1.11
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1.15
1.06
1.16
1.16
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1.08
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Question 4 (8 parts): A manufacturer's truck tire is designed to have a sidewall depth of 1.1 cm. If the sidewall is too deep, the tire will handle poorly; if the sidewall is too shallow, the tire will not be durable. Recently, customer complaints have led the manufacturer to suspect that its tires' sidewall depth may not meet the design specification u= 1.1 cm. Destructive testing is expensive, so the manufacturer has drawn a random sample of 50 tires from its production line which were cut open to measure sidewall depth. Depth measurements are recorded the Midterm Exam Workbook. a. Conduct the appropriate hypothesis test to determine whether there is strong evidence that sidewall depth is not in compliance with the manufacturer's specification. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one- tailed test to the right, or a two-tailed test? b. What is the p-value for the test statistic in (a)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). c. Based on the results from (a) and (b), what is your conclusion about the average tire sidewall depth at a = .05? d. Compute a 95% confidence interval for the average tire sidewall depth. e. Is your hypothesis test conclusion from (c) consistent with the confidence interval in (d)? Why or why not? f. Now conduct the different hypothesis test to determine whether there is strong evidence to support the alternative hypothesis that the variance of the sidewall depth exceeds .001. Specifically, state the null hypothesis and then compute the relevant test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test? g. What is the p-value for the test statistic in (f)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). h. Based on the results from (f) and (g), what is your conclusion about the variance of sidewall depth at a = .05?
Transcribed Image Text:Question 4 (8 parts): A manufacturer's truck tire is designed to have a sidewall depth of 1.1 cm. If the sidewall is too deep, the tire will handle poorly; if the sidewall is too shallow, the tire will not be durable. Recently, customer complaints have led the manufacturer to suspect that its tires' sidewall depth may not meet the design specification u= 1.1 cm. Destructive testing is expensive, so the manufacturer has drawn a random sample of 50 tires from its production line which were cut open to measure sidewall depth. Depth measurements are recorded the Midterm Exam Workbook. a. Conduct the appropriate hypothesis test to determine whether there is strong evidence that sidewall depth is not in compliance with the manufacturer's specification. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one- tailed test to the right, or a two-tailed test? b. What is the p-value for the test statistic in (a)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). c. Based on the results from (a) and (b), what is your conclusion about the average tire sidewall depth at a = .05? d. Compute a 95% confidence interval for the average tire sidewall depth. e. Is your hypothesis test conclusion from (c) consistent with the confidence interval in (d)? Why or why not? f. Now conduct the different hypothesis test to determine whether there is strong evidence to support the alternative hypothesis that the variance of the sidewall depth exceeds .001. Specifically, state the null hypothesis and then compute the relevant test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test? g. What is the p-value for the test statistic in (f)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; enter the numbers you used). h. Based on the results from (f) and (g), what is your conclusion about the variance of sidewall depth at a = .05?
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