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A leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,460 miles. A random sample of 42 cars leased from this firm had a mean of 12,542 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2520 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. D=0 OSO D20 (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) |(e) Can we support the leasing firm's claim that the mean number of miles driven annually is less than 13,460 miles? O Yes ONo plo

A leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,460 miles. A random sample of 42 cars leased from this firm had a mean of 12,542 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2520 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. D=0 OSO D20 (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) |(e) Can we support the leasing firm's claim that the mean number of miles driven annually is less than 13,460 miles? O Yes ONo plo

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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**Statistical Testing for Leasing Firm Claims** **Problem Statement:** A leasing firm claims that the mean number of miles driven annually, \( \mu \), in its leased cars is less than 13,460 miles. A random sample of 42 cars leased from this firm had a mean of 12,542 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2,520 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05 level of significance? **Instructions:** Perform a one-tailed test. Complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) **Steps:** (a) **State the Hypotheses:** - Null hypothesis \( H_0 \): - Alternative hypothesis \( H_1 \): (b) **Determine the Type of Test Statistic to Use:** - Choose the appropriate test statistic from a dropdown menu (Z-test or T-test). (c) **Find the Value of the Test Statistic:** - Calculate (Round to three or more decimal places). (d) **Find the Critical Value:** - Determine the critical value (Round to three or more decimal places). (e) **Conclusion:** - Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 13,460 miles? - Yes ❑ - No ❑ **Symbols and Notation:** - \( \mu \) : Population mean - \( \sigma \) : Population standard deviation - \( x̄ \) : Sample mean - \( n \) : Sample size **Important Notes:** - Use appropriate statistical tables or software for determining critical values and test statistics. - Ensure data assumptions for the tests are met (normal distribution, known standard deviation, etc.).
Transcribed Image Text:**Statistical Testing for Leasing Firm Claims** **Problem Statement:** A leasing firm claims that the mean number of miles driven annually, \( \mu \), in its leased cars is less than 13,460 miles. A random sample of 42 cars leased from this firm had a mean of 12,542 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 2,520 miles. Assume that the population is normally distributed. Is there support for the firm's claim at the 0.05 level of significance? **Instructions:** Perform a one-tailed test. Complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) **Steps:** (a) **State the Hypotheses:** - Null hypothesis \( H_0 \): - Alternative hypothesis \( H_1 \): (b) **Determine the Type of Test Statistic to Use:** - Choose the appropriate test statistic from a dropdown menu (Z-test or T-test). (c) **Find the Value of the Test Statistic:** - Calculate (Round to three or more decimal places). (d) **Find the Critical Value:** - Determine the critical value (Round to three or more decimal places). (e) **Conclusion:** - Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 13,460 miles? - Yes ❑ - No ❑ **Symbols and Notation:** - \( \mu \) : Population mean - \( \sigma \) : Population standard deviation - \( x̄ \) : Sample mean - \( n \) : Sample size **Important Notes:** - Use appropriate statistical tables or software for determining critical values and test statistics. - Ensure data assumptions for the tests are met (normal distribution, known standard deviation, etc.).
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