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 46,300 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.) Part (a) Part (b) Part (c) Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X ~ , 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.) = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less. If H0 is false, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.If H0 is false, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less. Correct! A p-value is the probability that an outcome of the data will happen purely by chance when H0 is true. Part (g) Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision: Since ? < p-value, we do not reject the null hypothesis.Since ? > p-value, we do not reject the null hypothesis. Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the average life span of the tires is less than 50,000.There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.

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 46,300 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.) Part (a) Part (b) Part (c) Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X ~ , 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.) = Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less. If H0 is false, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.If H0 is false, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less. Correct! A p-value is the probability that an outcome of the data will happen purely by chance when H0 is true. Part (g) Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision: Since ? < p-value, we do not reject the null hypothesis.Since ? > p-value, we do not reject the null hypothesis. Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the average life span of the tires is less than 50,000.There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.

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Description: 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. O

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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Question

Part (a)
Part (b)
Part (c)
Part (d)

State the distribution to use for the test. (Round your answers to two decimal places.)

X
~

,
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.)
=
Part (f)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.

If
H₀
is true, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.If
H₀
is true, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less. If
H₀
is false, then there is a chance equal to the p-value that the average life span of a tire is not 46,300 miles or less.If
H₀
is false, then there is a chance equal to the p-value that the average life span of a tire is 46,300 miles or less.

Correct! A p-value is the probability that an outcome of the data will happen purely by chance when
H₀
is true.
Part (g)
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:

reject the null hypothesisdo not reject the null hypothesis

(iii) Reason for decision:

Since ? < p-value, we do not reject the null hypothesis.Since ? > p-value, we do not reject the null hypothesis.    Since ? < p-value, we reject the null hypothesis.Since ? > p-value, we reject the null hypothesis.

(iv) Conclusion:

There is sufficient evidence to conclude that the average life span of the tires is less than 50,000.There is not sufficient evidence to conclude that the average life span of the tires is less than 50,000.
Part (i)

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.)

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Part (a)

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Part (e)

Part (f)

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Part (i)

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