Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Salma is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance (in thousands of km) driven on them before they need to be replaced. In the company's testing lab, Salma tests a random sample of 13 Puma tires and a random sample of 15 Eternal tires. (These samples are chosen independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 57.38 with a sample variance of 6.50. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 51.73 with a sample variance of 70.58. Assume that the two populations of distances driven are approximately normally distributed. Can Salma conclude, at the 0.10 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.)
Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Salma is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance (in thousands of km) driven on them before they need to be replaced. In the company's testing lab, Salma tests a random sample of 13 Puma tires and a random sample of 15 Eternal tires. (These samples are chosen independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 57.38 with a sample variance of 6.50. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 51.73 with a sample variance of 70.58. Assume that the two populations of distances driven are approximately normally distributed. Can Salma conclude, at the 0.10 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.)
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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Transcribed Image Text:Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Salma is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance (in thousands of km) driven on them before they need to be replaced.
In the company's testing lab, Salma tests a random sample of 13 Puma tires and a random sample of 15 Eternal tires. (These samples are chosen independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 57.38 with a sample variance of 6.50. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 51.73 with a sample variance of 70.58.
Assume that the two populations of distances driven are approximately normally distributed. Can Salma conclude, at the 0.10 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.)
![**Hypothesis Testing: Comparing Means**
**Null and Alternative Hypotheses:**
- \( H_0: \, \mu_1 - \mu_2 = 0 \)
- \( H_1: \, \mu_1 - \mu_2 \neq 0 \)
**(b) Determine the Type of Test Statistic to Use:**
- Test Statistic Type: \( t \)
- Degrees of Freedom: 12
**(c) Find the Value of the Test Statistic:**
- [Input field for value, rounded to three or more decimal places]
**(d) Find the Two Critical Values:**
- Critical Values: [Input field 1] and [Input field 2], rounded to three or more decimal places
**(e) Conclusion at 0.10 Level of Significance:**
- Question: Can Salma conclude there is a difference between the mean distance (in thousands of km) driven on Puma tires before replacement and the mean distance driven on Eternal tires before replacement?
- Options: [ ] Yes [ ] No](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c2c6cdc-915f-4610-98be-7cdca3a0288d%2Fae18e051-65b1-4698-9860-996900fe09d0%2F6ldqppb_processed.png&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing: Comparing Means**
**Null and Alternative Hypotheses:**
- \( H_0: \, \mu_1 - \mu_2 = 0 \)
- \( H_1: \, \mu_1 - \mu_2 \neq 0 \)
**(b) Determine the Type of Test Statistic to Use:**
- Test Statistic Type: \( t \)
- Degrees of Freedom: 12
**(c) Find the Value of the Test Statistic:**
- [Input field for value, rounded to three or more decimal places]
**(d) Find the Two Critical Values:**
- Critical Values: [Input field 1] and [Input field 2], rounded to three or more decimal places
**(e) Conclusion at 0.10 Level of Significance:**
- Question: Can Salma conclude there is a difference between the mean distance (in thousands of km) driven on Puma tires before replacement and the mean distance driven on Eternal tires before replacement?
- Options: [ ] Yes [ ] No
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