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

Answer:

Answer:

A)  H0:  µ = 60,000, Ha:  µ ≠ 60,000

B) Read below

C) -0.01

D)  Fail to reject the null hypothesis

e) 0.4960

Step-by-step explanation:

a:  The manufacturer claims that the mean mileage IS 60,000.  Is means equals in math.  That's the claim, so a not equals to sign goes in the alternate hypothesis because if the amount is significantly more or significantly less, then the claim is not correct.  

b: This is a 2 tailed test.  At a 0.05 significance level with a sample size of 48, our critical values are z < -1.96 and z > 1.96.  If our test statistic falls in either of these ranges, then we will reject the null hypothesis

c:  z = (59,500 - 60,000)/(5,000/√48) = -0.01

d:  -1.96 < -0.01 < 1.96, we fail to reject the null hypothesis

e:  P(z < -0.01) = 0.4960.  This means that a sample with these results can be expected to happen about 49.6% of the time

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