A metropolitan transportation authority has set a bus mechanical reliability goa

Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3, 900 bus miles. Bus mechanical reliability is measured 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. Find the test statistic for this hypothesis test. The critical value(s) for the test statistic is(are) 2.36 (Round to two decimal places as needed. Use a comma to separate answers as needed. Is there sufficient evidence to reject the null hypothesis using alpha = 0.01? A. 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. B. Do not reject 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 C. 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. D. Do not reject 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. Determine the p-value and interpret its meaning. The value is _

Explanation / Answer

From what I can understand, you need only the p value. I have also checked your answers for the test statistic, which is correct at 2.73, and the tcritical for a 1 tail, right tailed test for df = 99 is 2.36

Since tobserved(2.73) is > tcritical(2.36), you have correctly rejected H0 with the correct conclusion in OPTION C.

Now the p value, can either be found using a calculator or by using the excel function TDIST(2.73,99,1), which is the test statistic, df, tails. This returns the value of the right tail probability(which is what we need based on the alternative being a right tailed hypothesis) = 0.003749

Rounding to 3 decimal places, the required probability is 0.004.

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