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 3,875 bus miles and a sample standard deviation of 275 bus miles.

population of bus miles is more than 3,800 (use a 0.01 level of significance)

(a) find the critical value(s) for the test statistic is(are) _

(b) is there sufficient evidence to reject the null hypothesis using a=0.01

(c) Determine the p-value and interpret its meaning

Answer 1

Solution:

Given that:

= 3875 bus miles

s =275 bus miles

n = 100

Hypothesis:

H0 : 3800 bus miles

Ha :   3800 bus miles

a) Critical value :

degrees of freedom = d.f= n-1 = 100 - 1= 99

level of significance

= 0.01

tc = t0.01,99 = 2.365

Decision region: Reject H0 if t > tc = 2.365

Test statistic:

t = ( - ) / (s /n)

t = ( 3875- 3800) / (275 /100 )

t = 2.727

t = 2.727 > tc = 2.365 , so reject H0

b )There sufficient evidence to reject the null hypothesis using =0.01

c) P-value = 0.0038

The result is signifcant at P-value < 0.01

Reject H0

population of bus miles is more than 3,800