Question

# The Los Angeles County Metropolitan Transportation Authority has set a bus mechanical reliability goal of 3,900...

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. At 0.01 level of significance, is there evidence that the population mean bus miles is greater than 3,900 bus miles? Please show your work. Thank you!

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Given that

µ=3900, number=100, Xbar=3975, SD=275 LOS=0.01

Critical value=Z0.01=2.576

Null hypothesis: µ=3900

Alternative hypothesis: µ>3900

Test statistics = Xbar - u /(SD/SQRT(N)

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

Rejection rule is that if null hypothesis for test statistic > Critical value

We can infer that since Z=2.7272> Z0.01=2,576 we reject the null hypothesis 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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