Question

1. The longevity of truck tires (in thousands of miles) follows a normal distribution with mean µ and standard deviation σ = 20. Suppose n = 64 tires are randomly selected and the sample mean ¯ x = 76.5.

(a) Test H0 : µ = 75 versus Ha : µ 6= 75 at the α = 0.05 significance level using a 3-step test.

(b) Based upon your answer in part (a), does µ significantly differ from 75? Why?

(c) Find the p−value for the test in part (a).

Answer 1

Solution-a:

Ho:mu=75

Ha:mu not =75

alpha=0.05

z=xbar-mu/sigma/sqrt(n)

z=(76.5-75)/(20/sqrt(64))

z= 0.6

z crit for 95%

=NORM.S.INV(0.975)

=1.959963985

z critical values are -1.96 and +1.96

since z statistic is less than critical z value

Fail to reject Ho

Accept Ho

(b) Based upon your answer in part (a), does µ significantly differ from 75? Why?

test statisitc,z < critical z value

0.6<1.96

since we have not rejected Ho

Accepted Ho

µ does not significantly differ from 75.

(c) Find the p−value for the test in part (a).

p value for two tail is

2*left tail prob

left tail prob in excel is

=NORM.S.DIST(-0.6,TRUE)

=0.274253118
2*Left tail prob=2*0.274253118=0.548506236

p-value =0.5485

p>0.05

Fail to reject Ho

Accept Ho

There is no suffcient statistical evidence at 5% level of significance to conlcude that  µ significantly differ from 75

p-value =0.5485