Question

Which questions best describes: 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. 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. In order to assess the evidence, which question best describes what we need to determine? Group of answer choices If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be less than 5%? If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be 3.6% or less? If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be 5%? If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be less than 5%? If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be 3.6%?

Answer 1

Answer:

If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be 3.6% or less?

Step-by-step explanation:

First of all, when you want to contrast two hypothesis you need a confidence level p% without which the comparison makes no sense.

In this case, you want to refuse the null hypothesis (the average is 5%) with an alternative one (the average is less than 5%).  

You propose a new average (3.6%) based on the evidence.

You cannot prove that the average is actually 3.6%, but if you somehow determine that the probability the average is greater than 3.6% is lower than 100% minus your confidence level p% ,then you can refute the null hypothesis and accept the alternative one as new average.

So, from the possible choices, the one that fits the best is

If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be 3.6% or less?