When the workers for a major automobile manufacturer go on strike,there are repe

Question

When the workers for a major automobile manufacturer go on strike,there are
repercussions throughout the rest of the economy; in particular,the dealers who
sell the cars and trucks feel the pinch. Dealers like to maintain atwo-month
supply to give their customers adequate selection, but when themanufacturer
cannot deliver the vehicles, inventories dwindle. Shortly after aUnited Auto
Workers strike, the June 1998 days’ supply of these truckshad dropped to a
mean of 38 and a standard deviation of 16. Suppose one month afterthe strike
was settled, 15 dealers are sampled and the S-10 inventoriesyielded a mean
days’ supply of 45 trucks. Based on this new evidence, isthere enough evidence
at the 5% level of significance to suggest that the meandays’ supply after the
strike is greater than 38 vehicles.
a. Symbolize the null and alternative hypotheses.
b. Calculate the value of the test statistic. Round to 2 placesafter the decimal
point.
c. Find the p-value.
d. At the 0.05 level of significance, there _________ enoughevidence to suggest
that the mean days’ supply after the strike is greater than38 trucks.

Explanation / Answer

H0: The mean supply of trucks one month after the strike is thesame as the mean supply of trucks immediately after the strike. Ha: The mean supplies are different. z = (45 - 38) / (16 / sqrt(15)) = 1.694 --> p = .9545 Since we're conducting a 2-sided test, p_crit is .975. Thus,since .9545 < .975, we cannot conclude the mean supply isdifferent. Note: While it may be tempting to use a 2-sided test here, they aretypically avoided as they can be interpreted as a sign of bias bythe researcher (as they effectively provide the experiment withtwice as much of a tail to reach).

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