Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,700 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 3,775 bus miles and a sample standard deviation of 325 bus miles.

a. Is there evidence that the population mean bus miles is more than 3,700 bus miles? (Use a 0.10 level of significance.) State the null and alternative hypotheses.

b. Find the test statistic for this hypothesis test.

c. The critical value(s) for this test statistic is(are)

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

Answer 1

Solution :

= 3,700

=3,775

S =325

n = 100

a ) This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 3,700

Ha : > 3,700

b ) Test statistic = t

= ( - ) / S / n

= (3,775 - 3,700) / 325 / 100

= 2.308

Test statistic = t = 2.308

c ) The significance level is α =0.10, and the critical value for a right-tailed test is tc​ =1.29

d ) P-value =0.0115

= 0.10

P-value <

0.0115 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that