Stats

**Question:**

Suppose you work at a large tire distribution center. The tires’ average tread life has been 50,000 miles and a standard deviation of 5,000 miles. At the end of the year, the company can reevaluate their supply contract. There are four supply options for the next contract: the current supplier or one of three competitors.

The current supplier produces tires with an average tread life of 50,000 miles with a standard deviation of 5,000 miles. Competitor A claims to produce tires with an average tread life of 52,000 miles with a population standard deviation of 8,000 miles. Competitor B claims to produce tires with an average tread life of 50,000 miles with a population standard deviation of 3,000 miles. Competitor C claims to produce tires with an average tread life of 60,000 miles with a population standard deviation of 12,000 miles.

Use the following data to evaluate the claims of the three competitors. Use the Excel functions discussed in the book and in the labs for your calculations. **Be sure to round your answers to three decimal places.**

1. Consider Competitor A. Assume that the true mean is 52,000 miles and the population standard deviation is 8,000 miles. What is the standard error of the mean?

2. Consider Competitor A. Assume that the true mean is 52,000 miles and the population standard deviation is 8,000 miles. What is the z-score associated with the sample mean of 54,028.4 miles?

3. Consider Competitor A. Assume that the true mean is 52,000 miles and the population standard deviation is 8,000 miles. What is the probability that the sample mean for Competitor A is greater than 54,028.4 miles?

4. Based on your evaluation, is Competitor A’s claim valid? Why? (Hint: Your explanation should use the probability calculated above.)

5. Consider Competitor B. Assume that the true mean is 50,000 miles and the population standard deviation is 3,000 miles. What is the standard error of the mean?

6. Consider Competitor B. Assume that the true mean is 50,000 miles and the population standard deviation is 3,000 miles. What is the z-score associated with the sample mean of 50,407.686 miles?

7. Consider Competitor B. Assume that the true mean is 50,000 miles and the population standard deviation is 3,000 miles. What is the probability that the sample mean for Competitor B is greater than 50,407.686 miles?

8. Based on your evaluation, is Competitor B’s claim valid? Why? (Hint: Your explanation should use the probability calculated above.)

9. Consider Competitor C. Assume that the true mean is 60,000 miles and the population standard deviation is 12,000 miles. What is the standard error of the mean?

10. Consider Competitor C. Assume that the true mean is 60,000 miles and the population standard deviation is 12,000 miles. What is the z-score associated with the sample mean of 63,478.371 miles?

11. Consider Competitor C. Assume that the true mean is 60,000 miles and the population standard deviation is 12,000 miles. What is the probability that the sample mean for Competitor C is greater than 63,478.371 miles?

12. Based on your evaluation, is Competitor C’s claim valid? Why? (Hint: Your explanation should use the probability calculated above.)