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Randy Race owns a sneaker manufacturing company called Sole Man. Randy’s sneakers are sold in retail outlets located in New Jersey and New York.

**New Jersey**

There are 2,500 retail outlets that stock and sell Randy’s shoes in state of New Jersey. Randy contacted 100 of these stores at random and inquired as to how many boxes of sneakers they planned to order next month. The average of the sample was 18 boxes per store with a sample standard deviation of 6.

Construct a 68% confidence interval on the **average number of boxes of sneakers ordered per store** in the state of New Jersey next month.

If Randy wants to be 93% sure that he has enough boxes for **all the stores in the state of New Jersey**, how many should he manufacture?

**New York**

There are 3,000 retail outlets that stock and sell Randy’s sneakers in the state of New York. Randy sampled 100 of these and found that the average number of boxes of sneakers that would be ordered next month was 20 boxes with a standard deviation of 8.

Can Randy prove that the average number of boxes of sneakers sold per store is lower in New Jersey than it is in New York at the .05 level of significance? (What are the null and the alternative hypotheses. **Plug the values into the Z _{TEST }formula**. Use Z

(Do Last) To motivate the sales staff in New York, Randy promised to give them a bonus if the sales in the state of New York exceed 57,000 boxes next month. Can Randy prove to his sales staff that they will get a bonus at the .10 level of significance? What are the null and the alternative hypotheses. **Plug the values into the Z _{TEST }formula**. Use Z

To construct a 68% confidence interval on the average number of boxes of sneakers ordered per store in the state of New Jersey next month, we'll use the following information: Sample mean (x?) = 18 Sample standard deviation (s) = 6 Sample size (n) = 100 The formula to calculate the confidence interval is:

The Z-value for a 68% confidence interval is 1.00 (since it covers 34% on each side of the mean). Plugging in the values:

CI = 18 ± (1.00 * 0.6)

CI = 18 ± 0.6

CI = (17.4, 18.6) Therefore, the 68% confidence interval on the average number of boxes of sneakers ordered per store in the state of New Jersey next month is (17.4, 18.6) boxes. To be 93% sure that he has enough boxes for all the stores in New Jersey, Randy needs to determine the critical value associated with a 93% confidence interval. Using a standard normal distribution table or calculator, the critical value for a 93% confidence interval is approximately 1.81. The margin of error (ME) is given by the formula:

ME =

ME = 1.81 * 0.6

ME ? 1.09

Refer above solution