In a study of distances traveled by buses before the first major engine failure,a sample of 191 buses results in a mean of 96,700 miles and a standard deviation of 37,500 miles.Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.
A)0.0000
B)0.0068
C)-0.0068
D)0.0136
E)-0.0136

Question

Quizplus · Accepted Answer

We will use a one-sample t-test with the null and alternative hypotheses as follows:

Null hypothesis: μ ≤ 90,000
Alternative hypothesis: μ > 90,000

The test statistic is given by:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (96,700 - 90,000) / (37,500 / sqrt(191)) ≈ 1.96

The degrees of freedom for this test are df = n-1 = 190.

Using a t-table or calculator, the corresponding p-value for a one-tailed test with df = 190 and t = 1.96 is approximately 0.0068.

Therefore, the answer is B.

In a Study of Distances Traveled by Buses Before the First