Question

A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses. H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05. Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.
What assumption about the sample underlies the hypothesis test?

a.The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.

b.The sample comes from a population of tires with 60,000 miles where 3.6% of the tires are worn out.

c.The sample comes from a population of tires where 250 are used for 60,000 miles.

d.The sample comes from a population of 250 tires that have a 60,000 mile warranty.

Answer 1

Answer:

(A)The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.

Step-by-step explanation:

The tire manufacturer has a 60,000 mile warranty for tread life. To verify the authenticity of its claim, it picks a sample of 250 tires (out of the population of tires) that have been used for 60,000 miles.  

Given the hypothesis:

$H_0$: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.  

$H_a$: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

It is assumed that 5% of the tires in the sample are worn out and the hypothesis is formulated to prove or disprove this assumption.