A metropolitan transportation authority has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,975 bus miles and a sample standard deviation of 275 bus miles. Complete parts(a) and(b) below.

a. Is there evidence that the population mean bus miles is more than 3,900 busmiles? (Use a 0.01 level ofsignificance.)

State the null and alternative hypotheses.

H0: (1)

H1: (2)

(Type integers ordecimals.)

Find the test statistic for this hypothesis test.

tSTAT= (Round to two decimal places asneeded.)

The criticalvalue(s) for the test statisticis(are) .

(Round to two decimal places as needed. Use a comma to separate answers asneeded.)

Is there sufficient evidence to reject the null hypothesis using =0.01?

A. Donotreject the null hypothesis. There is insufficient evidence at the 0.01 level of significance that the population mean bus miles is less than 3,900 bus miles.

B. Reject the null hypothesis. There is sufficient evidence at the 0.01 level of significance that the population mean bus miles is greater than 3,900 bus miles.

C. Reject the null hypothesis. There is sufficient evidence at the 0.01 level of significance that the population mean bus miles is less than 3,900 bus miles.

D. Donotreject the null hypothesis. There is insufficient evidence at the 0.01 level of significance that the population mean bus miles is greater than 3,900 bus miles.

b. Determine thep-value and interpret its meaning.

Thep-value is .

(Round to three decimal places asneeded.)

What does thisp-value mean given the results of part(a)?

A. Thep-value is the probability that the actual mean is 3,900 bus miles or greater given the sample mean is 3,975 bus miles.

B. Thep-value is the probability that the actual mean is 3,975 bus miles or less.

C.Thep-value is the probability of getting a sample mean of 3,975 bus miles or greater if the actual mean is 3,900 bus miles.

D.Thep-value is the probability that the actual mean is greater than 3,975 bus miles.

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(2)

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