Question

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 8000. A survey of owners of that tire design is conducted. Of the 27 tires in the survey, the average lifespan was 45,900 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level?

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.)

What is the test statistic? (Round your answer to two decimal places.)

Answer 1

@sillybilly123 I don't remember how to do this would you mind assisting?

Answer 2

suresy, i will - with pleasure. this is a killer qu at AP level

Answer 3

the claim is that:

\(H_o: \qquad \mu = 50,000\)

the alternative-claim is that:

\(H_1: \qquad \mu < 50,000\)

And there is also \(\sigma = 8,000\)

There is a survey with \(n = 27 < 30\) <-- no Central Limit Theorem

AND, from the survey:

\(\qquad \bar x = 45,900, \quad s = 9,800\)


BIG QUESTION: Do the data support the claim at the 5% level?


ie \(\alpha = 5 \%\)

The Student-t ?? Because \(n \approx 30\), it mght make sense to go through both approches

Answer 4

Jayster: option to edit posts?!?