The Los Angeles County Metropolitan Transportation Authority has set a bus mecha

Question

The Los Angeles County 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.

a. Is there evidence that the population mean bus miles is more than 3,900 bus miles? ( Use a 0.05 level of significance.

b. determine the p-value and interpret its meaning

Please show detail in how you came to your answers.

Explanation / Answer

solution:

a.USE CRITICAL VALUE METHOD to solve

µ=3900, n=100, X-bar=3975, S=275 =0.05

Critical value=Z0.025=1.96

H0: µ=3900

Ha: µ>3900

Test statistics

Z=(3975-3900)/(275/100) = 2.7272

Rejection rule: Reject H0 if test statistics > Critical value

Decision and conclusion: Since Z=2.7272> Z0.025=1.96 e reject H0 and conclude that there is enough evidence to support the claim that the population mean bus miles is more than 3,900 bus miles

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