Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Ann is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in th mean distance (in thousands of km) driven on them before they need to be replaced. E In the company's testing lab, Ann tests a random sample of 14 Puma tires and a random sample of 15 Eternal tires. (These samples are chose independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 54.71 with a sample variance of 5.95. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 50.21 with a sample variance of 37.75. Assume that the two populations of distances driven are approximately normally distributed. Can Ann conclude, at the 0.05 level of significance, that there is a difference between the population mean of the distances (in thousands of km) driven on Puma tires before they need to be replaced and the population mean of the distances (in thousands of km) driven on Eternal tires before they need to be replaced? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternate hypothesis H₁. H₂ : O H₁0 (b) Determine the type of test statistic to use. Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) and (e) At the 0.05 level of significance, can Ann conclude that there is a difference between the mean distance (in thousands of km) driven on Puma tires before they need to be replaced and the mean distance (in thousands of km) driven on Eternal tires before they need to be replaced? OYes No 1 |x 5 0=0 D X S 2 0*0 O0

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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$**Comparative Analysis of Tire Brands for Tractor-Trailers** **Overview:** This study compares two popular brands of tractor-trailer tires: Puma and Eternal. Ann, a buyer for a shipping company, conducts this analysis to determine if there is a significant difference in the mean distance (in thousands of kilometers) that can be driven on each brand before needing replacement. **Testing Details:** In the lab, Ann tests a random sample of 14 Puma tires and 15 Eternal tires. - **Puma Tires:** - Sample Mean Distance: 54.71 (thousands of km) - Sample Variance: 5.95 - **Eternal Tires:** - Sample Mean Distance: 50.21 (thousands of km) - Sample Variance: 37.75 **Objective:** Determine if there is a statistical difference in the mean distances driven on these tires at a 0.05 significance level. Assume distance distributions are normally distributed. **Methodology:** Perform a two-tailed test with the following components: 1. **Hypotheses:** - Null Hypothesis $ H_0 $: There is no difference in the mean distances. - Alternate Hypothesis $ H_1 $: There is a difference in the mean distances. 2. **Test Statistic:** - Use a t-test to compare the means. - Compute the degrees of freedom. 3. **Data Analysis:** - Calculate the test statistic value (round to three decimal places). - Determine critical values (round to three decimal places). 4. **Conclusion:** - Based on the 0.05 significance level, conclude whether there is a significant difference in the performance of Puma and Eternal tires. This comparative study aids in making informed purchasing decisions based on tire longevity.$

Transcribed Image Text:**Comparative Analysis of Tire Brands for Tractor-Trailers** **Overview:** This study compares two popular brands of tractor-trailer tires: Puma and Eternal. Ann, a buyer for a shipping company, conducts this analysis to determine if there is a significant difference in the mean distance (in thousands of kilometers) that can be driven on each brand before needing replacement. **Testing Details:** In the lab, Ann tests a random sample of 14 Puma tires and 15 Eternal tires. - **Puma Tires:** - Sample Mean Distance: 54.71 (thousands of km) - Sample Variance: 5.95 - **Eternal Tires:** - Sample Mean Distance: 50.21 (thousands of km) - Sample Variance: 37.75 **Objective:** Determine if there is a statistical difference in the mean distances driven on these tires at a 0.05 significance level. Assume distance distributions are normally distributed. **Methodology:** Perform a two-tailed test with the following components: 1. **Hypotheses:** - Null Hypothesis $ H_0 $: There is no difference in the mean distances. - Alternate Hypothesis $ H_1 $: There is a difference in the mean distances. 2. **Test Statistic:** - Use a t-test to compare the means. - Compute the degrees of freedom. 3. **Data Analysis:** - Calculate the test statistic value (round to three decimal places). - Determine critical values (round to three decimal places). 4. **Conclusion:** - Based on the 0.05 significance level, conclude whether there is a significant difference in the performance of Puma and Eternal tires. This comparative study aids in making informed purchasing decisions based on tire longevity.

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