Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,900

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 3,925 bus miles and a sample standard deviation of 225 bus miles. Complete parts​ (a) and​ (b) below.

a. Is there evidence that the population mean bus miles is more than 3,900

bus​ miles? (Use a 0.10 level of​ significance.)

State the null and alternative hypotheses.

b. tSTAT =

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 3900

H_a : > 3900

Test statistic = t

= ( - ) / s / n

= (3925 - 3900) / 225 / 100

t STAT = Test statistic = 1.11

df = 99

P-value = 0.1348

= 0.10

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the population mean bus miles is more than 3,900 bus​ miles .