Question

Larry Bomser has been asked to evaluate sizes of tire inventories for retail outlets of a major tire manufacturer. From a sample of 120 stores, he has found a mean of 310 tires. The industry average is 325. If the standards deviation for the sample was 72, would you say that the inventory level maintained by this manufacturer is significantly different from the industry norm? Explain why. (Use a 95 percent confidence level.)

Answer 1

Using a hypothesis test for the sample mean, a Z-score of -2.28 corresponds to a p-value less than 0.05, indicating that the inventory level is significantly different from the industry average at the 95% confidence level.

Step-by-step explanation:

To assess whether the tire inventory level maintained by this manufacturer is significantly different from the industry norm, we would use a hypothesis test for the sample mean with a 95 percent confidence level. First, we calculate the Z-score using the formula:

Z = (Sample mean - Population mean) / (Standard deviation / sqrt(n))

For Larry Bomser's evaluation, this would be:

Z = (310 - 325) / (72 / sqrt(120))

Z = -15 / (72 / 10.954) = -15 / 6.576 = -2.28

Next, we look up the Z-score in z-tables, or use a statistical software to find the p-value. If the p-value is less than the alpha level of 0.05 (since we're using a 95% confidence level), we conclude the inventory level is significantly different from the industry norm. Otherwise, we do not have enough evidence to say it is significantly different.

Since the Z-score of -2.28 corresponds to a p-value less than 0.05, we can conclude that the inventory level is significantly different from the industry average at the 95% confidence level.