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 mea 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.) O Part (a) O Part (b) O Part (c) O Part (d) O Part (e) O Part (n O Part (g) O Part (h) Indicate the correct decision ("reject" or "do not rejecr the null hypothesis), the reason for it, and write an appropriate conclusion. ) Alpha (Enter an exact number as an integer, fraction, or decimal.) (i) Decision: O reject the nul hypothesis O do not reject the null hypothesis (i) Reason for decision: O since a p-value, we do not reject the null hypothesis O Since a > p-value, we do not reject the null hypothesis. O Since a < p-value, we reject the null hypothesis. O Since a> p-value, we reject the null hypothesis. (iv) Conclusion: O There is sufficient evidence to conclude that the average life span of the tires is less than 50.000. O There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.

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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$### Tire Lifespan Statistical Claim Analysis **Problem Statement:** 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 8,000 miles. Using alpha $ \alpha = 0.05 $, is the data highly consistent with the claim? **Note:** If you are using a Student’s t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) --- ### Part (h) **Hypothesis Testing:** (i) **Alpha ($ \alpha $):** Enter an exact number as an integer, fraction, or decimal. - $ \alpha = $ (ii) **Decision:** Indicate whether to reject or not reject the null hypothesis. - $ \bigcirc $ Reject the null hypothesis - $ \bigcirc $ Do not reject the null hypothesis (iii) **Reason for Decision:** - $ \bigcirc $ Since $ \alpha < p $-value, we do not reject the null hypothesis. - $ \bigcirc $ Since $ \alpha > p $-value, we reject the null hypothesis. - $ \bigcirc $ Since $ \alpha < p $-value, we reject the null hypothesis. - $ \bigcirc $ Since $ \alpha > p $-value, we do not reject the null hypothesis. (iv) **Conclusion:** - $ \bigcirc $ There is sufficient evidence to conclude that the average life span of the tires is less than 50,000. - $ \bigcirc $ There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000. --- ### Part (i) **Confidence Interval Construction:** Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.) **Graph Description:** - The graph is a normal distribution curve labeled "95% C.I." - The curve represents a$

Transcribed Image Text:### Tire Lifespan Statistical Claim Analysis **Problem Statement:** 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 8,000 miles. Using alpha $ \alpha = 0.05 $, is the data highly consistent with the claim? **Note:** If you are using a Student’s t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) --- ### Part (h) **Hypothesis Testing:** (i) **Alpha ($ \alpha $):** Enter an exact number as an integer, fraction, or decimal. - $ \alpha = $ (ii) **Decision:** Indicate whether to reject or not reject the null hypothesis. - $ \bigcirc $ Reject the null hypothesis - $ \bigcirc $ Do not reject the null hypothesis (iii) **Reason for Decision:** - $ \bigcirc $ Since $ \alpha < p $-value, we do not reject the null hypothesis. - $ \bigcirc $ Since $ \alpha > p $-value, we reject the null hypothesis. - $ \bigcirc $ Since $ \alpha < p $-value, we reject the null hypothesis. - $ \bigcirc $ Since $ \alpha > p $-value, we do not reject the null hypothesis. (iv) **Conclusion:** - $ \bigcirc $ There is sufficient evidence to conclude that the average life span of the tires is less than 50,000. - $ \bigcirc $ There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000. --- ### Part (i) **Confidence Interval Construction:** Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.) **Graph Description:** - The graph is a normal distribution curve labeled "95% C.I." - The curve represents a

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