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 60,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,500 miles. Crosset would like to know if their experience is different from the manufacturer’s claim.

1. State the null hypothesis and the alternate hypothesis.

2. State whether the decision rule is true or false: Reject H₀ if z < −1.96 or z > 1.96 using a 0.05 significance level.

	True
	False

3. Compute the value of the test statistic.  (Round your answer to 3 decimal places.)

4. What is your decision regarding H₀?

	Reject H0
	Do not reject H0

5. What is the p-value?  (Round answer to 4 decimal places.)

6. Is Crosset's experience different from that claimed by the manufacturer at the 0.05 significance level?

	Yes
	No

Answer 1

a )

H0: = 60000

Ha: 60000

b)

Decision rule = reject H0 if z < -1.96 or z > 1.96

True.

c)

Test statistics

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

= -0.693

d)

Since test statistics falls in non-rejection region, Do not reject H0

e)

p-value = 2 * P( Z < z)

= 2 * P( Z < -0.693)

= 2 * 0.2442

= 0.4884

f)

No,