Question

The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59500 miles. Is Crosset’s experience different from that claimed by the manufacturer at the 0.05 significance level? For this question, you must (a) state the null and alternative hypotheses, (b) state the decision rule, (c) compute the value of the test statistic, (d) make the decision regarding the null hypothesis, and (e) determine the p-value.

Answer 1

Ans:

a)

b)

critical z values=+/-1.96

Decision rule:

Reject H₀,if z<-1.96 or z>1.96

c)Test statistic:

z=(59500-60000)/(5000/sqrt(48))

z=-0.693

d)Fail to reject H₀.

e)

p-value=2*P(z<-0.693)=0.4884