Question

1)One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire.  The warranty is for 40,000 miles.  The tire company believes that the tire actually lasts more than 40,000 miles.  A sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of 15,000 miles.  Test the hypothesis with a 0.05 significance level.

Complete your answers with the following responses:  (1) 2.33, (2) H_o: µ = 40,000, (3) t-test, (4) H_a: µ > 40,000, (5) Reject H_o if |t_Calculated| > t_Critical,; Do not Reject H_o otherwise, or (6) Reject H_o

What is the calculated value of t?

2) One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire.  The warranty is for 40,000 miles.  The tire company believes that the tire actually lasts more than 40,000 miles.  A sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of 15,000 miles.  Test the hypothesis with a 0.05 significance level.

Complete your answers with the following responses:  (1) 2.33, (2) H_o: µ = 40,000, (3) t-test, (4) H_a: µ > 40,000, (5) Reject H_o if |t_Calculated| > t_Critical,; Do not Reject H_o otherwise, or (6) Reject Ho

This is an example of what type of test?

3)One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire.  The warranty is for 40,000 miles.  The tire company believes that the tire actually lasts more than 40,000 miles.  A sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of 15,000 miles.  Test the hypothesis with a 0.05 significance level.

Complete your answers with the following responses:  (1) 2.33, (2) H_o: µ = 40,000, (3) t-test, (4) H_a: µ > 40,000, (5) Reject H_o if |t_Calculated| > t_Critical,; Do not Reject H_o otherwise, or (6) Reject H_o

What is the decision rule?

Answer 1

1)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (45000 - 40000)/(15000/sqrt(49))
t = 2.33

2)

This is an example of t test

3)

Rejection Region
This is right tailed test, for α = 0.05 and df = 48
Critical value of t is 1.677.
Hence reject H0 if t > 1.677

Reject Ho if |tCalculated| > tCritical,; Do not Reject Ho otherwise, or