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. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles. Do the data support the claim at the 5% level?

Answer 1

Given:

= 50,000, n = 28, = 46,500, = 8000, = 5% = 0.05

Hypothesis:

Ho: = 50,000

Ha: < 50,000

Test statistic:

Critical value:

Z =Z0.05 = -1.645              ..................Using standard Normal table

Decision Rule:

Z < Z /2 , Then Reject Ho at % level of significance.

Conclusion:

Z < Z , i.e. -2.32 < -1.645, That is Reject Ho at 5% level of significance.

Therefore, Its deluxe tire averages at least 50,000 miles before it needs to be replaced.