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 appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.
A)2.47
B)34.13
C)478.16
D)-34.13
E)-2.47

Question

Quizplus · Accepted Answer

To test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles, we can use a one-sample t-test. The null hypothesis is that the true mean distance traveled is equal to 90,000 miles, and the alternative hypothesis is that it is greater than 90,000 miles.

The formula for the t-test statistic for a one-sample test is:

t = (sample mean - hypothesized mean) / (standard error of the mean)

In this case, the hypothesized mean is 90,000 miles, the sample mean is 96,700 miles, and the standard error of the mean is:

SE = standard deviation / sqrt(sample size)
SE = 37,500 / sqrt(191)
SE = 2718.85

Plugging in the numbers, we get:

t = (96,700 - 90,000) / 2718.85
t = 2.47

Therefore, the appropriate test statistic is 2.47, which corresponds to answer choice A.

In a Study of Distances Traveled by Buses Before the First