Question

Tire Life Prompt:

A major tire manufacturer claims their heavy-duty truck tires have an average usage life of 71,000 miles. The shipping department of the company you work for has been using these tires for several years and feels they are not getting the mileage promised. The manager pulled 25 maintenance records and found an average tire life of 68,050 miles, with a standard deviation of 11,602 miles. He asks you to conduct a test of hypothesis to determine if the actual life of the tires is less than the manufacturer's claim.

Response Parameters

Use what you have learned about hypothesis testing to answer the following questions.

What type of test should you perform? Which of the three equations for hypothesis testing should you use? Why did you choose that one? You may assume tire life is normally distributed.

State your null and alternate hypotheses. Why did you choose those values and mathematical operators?

What is the value of your test statistic? (Clearly, show how you arrived at this value.)

Interpret the test statistic: Choose an appropriate confidence level, then evaluate the test statistic using either the critical value or the p-value approach. Why did you choose the confidence level that you did?

Clearly, state the outcome of your test of hypothesis.

What does your outcome mean in statistical terms?

What does your outcome mean in terms of the problem?

Answer #1

A manufacturer claims that the life span of its tires is
52,000 miles. You work for a consumer protection
agency and you are testing these tires. Assume the life spans of
the tires are normally distributed. You select 100
tires at random and test them. The mean life span is
51.831 miles. Assume sigma = 800.
Complete parts (a) through (c).
(a) Assuming the manufacturer's claim is correct, what
is the probability that the mean of the sample is
51,831...

A manufacturer claims that the life span of its tires is
52 comma 00052,000
miles. You work for a consumer protection agency and you are
testing these tires. Assume the life spans of the tires are
normally distributed. You select
100100
tires at random and test them. The mean life span is
51 comma 79951,799
miles. Assume
sigma?equals=700700.
Complete parts? (a) through? (c).
?(a) Assuming the? manufacturer's claim is? correct, what is the
probability that the mean of the sample...

A manufacturer claims that the life span of its tires is 52
comma 000 miles. You work for a consumer protection agency and you
are testing these tires. Assume the life spans of the tires are
normally distributed. You select 100 tires at random and test them.
The mean life span is 51 comma 729 miles. Assume sigmaequals900.
Complete parts (a) through (c). (a) Assuming the manufacturer's
claim is correct, what is the probability that the mean of the
sample...

A manufacturer claims that the life span of its tires is
48,000
miles. You work for a consumer protection agency and you are
testing these tires. Assume the life spans of the tires are
normally distributed. You select
one hundred
tires at random and test them. The mean life span is
47,858
miles. Assume
sigmaσequals=900
Complete parts (a) through (c).
(a) Assuming the manufacturer's claim is correct, what is the
probability that the mean of the sample is
47,858
miles...

A tire manufacturer claims that his tires have a mean life of
60,000 miles when used under normal driving conditions. A firm that
requires a larger number of these tires wants to test the claim. If
the claim is correct, the firm will purchase the manufacturer’s
tires; otherwise, the firm will seek another supplier. Now a random
sample of 100 tires is taken and the mean and standard deviation of
the 100 tires are found. Using these sample results, a...

A tire manufacturer claims that his tires have a mean life of
60,000 miles when used under normal driving conditions. A firm that
requires a larger number of these tires wants to test the claim. If
the claim is correct, the firm will purchase the manufacturer’s
tires; otherwise, the firm will seek another supplier. Now a random
sample of 100 tires is taken and the mean and standard deviation of
the 100 tires are found. Using these sample results, a...

A tire manufacturer claims that his tires have a mean life of
60,000 miles when used under normal driving conditions. A firm that
requires a larger number of these tires wants to test the claim. If
the claim is correct, the firm will purchase the manufacturer’s
tires; otherwise, the firm will seek another supplier. Now a random
sample of 100 tires is taken and the mean and standard deviation of
the 100 tires are found. Using these sample results, a...

A tire company claims that their new tires will have an average
life of 139000 miles. A consumer group wishes to test that this
claim is not true at the α = 0.05 level of significance. a) Which
would be the correct hypotheses for this test? H 0 : μ = 139000 , H
A : μ < 139000 H 0 : μ = 139000 , H A : μ ≠ 139000 H 0 : p =
139000 , H...

A tire manufacturer produces tires that have a mean life of at
least 20000 miles when the production process is working properly.
The operations manager stops the production process if there is
evidence that the mean tire life is below 20000 miles.
To monitor the production process, the operations manager takes
a random sample of 15 tires each week and subjects them to
destructive testing. They calculate the mean life of the tires in
the sample, and if it is...

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