MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 30 tires surveyed, the mean lifespan was 46,100 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
---
### Parts of the Problem:
**Part (a):**
(Not specified in the provided text.)
**Part (b):**
(Not specified in the provided text.)
**Part (c):**
(Not specified in the provided text.)
---
**Part (d):**
**State the distribution to use for the test.** (Round your answers to two decimal places.)
\[
\bar{X} \sim ( \text{Answer: } \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ )
\]
---
**Part (e):**
**What is the test statistic?** (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
\[ \text{Select the distribution: } \_\_\_\_\_\_\_ = \]
---
**Part (f):**
**What is the p-value?** (Round your answer to four decimal places.)
\[ \_\_\_\_\_ \]
**Explain what the p-value means for this problem.**
- O If \( H_0 \) is true, then there is a chance equal to the p-value that the average life span of a tire is 46,100 miles or less.
- O If \( H_0 \) is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,100 miles or less.
- O If \( H_0 \) is false, then there is a chance equal to the p-value that the average life span of a tire is 46,100 miles or less.
- O If \( H_0 \) is false, then there is a chance equal to the p-value that the average life](https://content.bartleby.com/qna-images/question/0cc22df3-bc64-47be-bc98-9601b5672ba2/de6741aa-8d5e-4824-874d-e0a4e3d16a6d/m952bk6_processed.jpeg)
Transcribed Image Text:A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 30 tires surveyed, the mean lifespan was 46,100 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?
Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
---
### Parts of the Problem:
**Part (a):**
(Not specified in the provided text.)
**Part (b):**
(Not specified in the provided text.)
**Part (c):**
(Not specified in the provided text.)
---
**Part (d):**
**State the distribution to use for the test.** (Round your answers to two decimal places.)
\[
\bar{X} \sim ( \text{Answer: } \_\_\_\_\_\_\_ , \_\_\_\_\_\_\_ )
\]
---
**Part (e):**
**What is the test statistic?** (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
\[ \text{Select the distribution: } \_\_\_\_\_\_\_ = \]
---
**Part (f):**
**What is the p-value?** (Round your answer to four decimal places.)
\[ \_\_\_\_\_ \]
**Explain what the p-value means for this problem.**
- O If \( H_0 \) is true, then there is a chance equal to the p-value that the average life span of a tire is 46,100 miles or less.
- O If \( H_0 \) is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,100 miles or less.
- O If \( H_0 \) is false, then there is a chance equal to the p-value that the average life span of a tire is 46,100 miles or less.
- O If \( H_0 \) is false, then there is a chance equal to the p-value that the average life
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