A metropolitan transportation authority has set a bus mechanical reliability goa

Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 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 3,850 bus miles and a sample standard deviation of 175 bus miles. Complete parts (a) and (b) below.

Find the test statistic for this hypothesis test.

tSTAT =

b. Determine the p-value and interpret its meaning.

p-value =

Interpret the p-value's meaning given the results of part (a).

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 3,800

Alternative hypothesis: 3,800

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 17.5

DF = n - 1 = 100 - 1

D.F = 99

t = (x - ) / SE

t = 2.86

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 99 degrees of freedom is less than -2.86 or greater than 2.86.

Thus, the P-value = 0.0052

Interpret results. Since the P-value (0.0052) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that bus mechanical reliability goal is 3,800 bus miles.

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