A particular brand of tires advertises that its deluxe tire averages at least 50,000 miles before it needs to be replaced. However, a consumer group is challenging the advertisement and claims the tires last fewer than 50,000 miles From past studies of this tire, the population 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 45,700 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) State the null hypothesis. H0: ? = 50,000 H0: ? ≠ 50,000 H0: ? < 50,000 H0: ? ≥ 50,000 Part (b) State the alternative hypothesis. Ha: ? ≥ 50,000 Ha: ? = 50,000 Ha: ? < 50,000 Ha: ? ≠ 50,000 Part (c) In words, state what your random variable X represents. X represents the number of tires surveyed. X represents the average life span, in miles, of the tires surveyed. X represents the life span, in miles, for a tire. X represents the average life span, in years, of the tires surveyed. Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X - N (-------------, ------------------- ~ , 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.) t or Z = 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 false, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If if H0 is false, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less. If If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less

A particular brand of tires advertises that its deluxe tire averages at least 50,000 miles before it needs to be replaced. However, a consumer group is challenging the advertisement and claims the tires last fewer than 50,000 miles From past studies of this tire, the population 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 45,700 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) State the null hypothesis. H0: ? = 50,000 H0: ? ≠ 50,000 H0: ? < 50,000 H0: ? ≥ 50,000 Part (b) State the alternative hypothesis. Ha: ? ≥ 50,000 Ha: ? = 50,000 Ha: ? < 50,000 Ha: ? ≠ 50,000 Part (c) In words, state what your random variable X represents. X represents the number of tires surveyed. X represents the average life span, in miles, of the tires surveyed. X represents the life span, in miles, for a tire. X represents the average life span, in years, of the tires surveyed. Part (d) State the distribution to use for the test. (Round your answers to two decimal places.) X - N (-------------, ------------------- ~ , 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.) t or Z = 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 false, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If if H0 is false, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less. If If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If If H0 is true, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Part (a)

State the null hypothesis.

H₀:
? = 50,000
H₀:
? ≠ 50,000
H₀:
? < 50,000
H₀:
? ≥ 50,000
Part (b)

State the alternative hypothesis.

H_a: ? ≥ 50,000

H_a: ? = 50,000

H_a: ? < 50,000

H_a: ? ≠ 50,000
Part (c)

In words, state what your random variable X represents.

X represents the number of tires surveyed.

X represents the average life span, in miles, of the tires surveyed.

X represents the life span, in miles, for a tire.

X represents the average life span, in years, of the tires surveyed.
Part (d)

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

X - N (-------------, -------------------

~

,
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.)

t

or

Z

=
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 false, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If
if H₀ is false, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less. If

If H₀ is true, then there is a chance equal to the p-value that the average life span of a tire is not 45,700 miles or less.If

If H₀ is true, then there is a chance equal to the p-value that the average life span of a tire is 45,700 miles or less.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.
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 hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? < p-value, we reject the null hypothesis.

Since ? > p-value, we reject the null hypothesis.

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

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

(iv) Conclusion:
There is sufficient evidence to support the claim that the average life span of the tires is less than 50,000.

There is not sufficient evidence to support the claim that the average life span of the tires is less than 50,000.

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.

Expert Solution