1. You are responsible for human resources at a large retailer, and recently, you have found that several of your hires seem to be leaving earlier than expected. In the past, the average tenure of a new graduate was 2.2 years. Tenure is approximately mound-shaped, so you assume the distribution is normally distributed. You gather a sample of the most recent new hires' tenure (that have all left, so you don't have truncated data), and find that the standard deviation is 1.1 years in a sample of 25. The sample mean was 2.0.

1. Construct a 95% confidence interval for the mean tenure of new-grad hires.
2. Interpret the confidence interval.
3. What is the probability that the population mean falls within the confidence interval?
4. What proportion of the parent population falls within the confidence interval?
5. Does the confidence interval allow you to state that the mean has changed from the past
6. average tenure? Why or why not?

Assume you wish to perform a formal hypothesis test to show that the mean has fallen from the past average tenure. You want to be quite certain, so you require a significance level of 1%.

f. What sample size is required, provided you use the sample mean and sample standard deviation from the sample above as planning values? (2 pts.)

Assume in the following that you gather a sample of 200, with a mean of 1.99 and a standard deviation of 1.15.

1. What are the appropriate hypotheses?
2. What is the rejection region (RR)?
3. What is the value of the standardized test statistic (STS)?
4. What is your conclusion?
5. What does your conclusion tell you about the p-value?
6. What is the p-value?

2. Continuing from above, you are also concerned about the proportion of individuals that have had to be let go. Drawing from all the individuals who have left the company in the last decade, you find that the proportion who were let go was 0.15. In the last year, you took a random sample from the employees that left and found the proportion was 0.20. The sample size was 20.

1. Was your sample size large enough to use the normal approximation to the binomial distribution? Why or why not?
2. You increased your sample size to the minimum amount that would support using the normal approximation, assuming the sample proportion remained unchanged at 0.20. What is that sample size?
3. With the sample size determined in part (b), the sample proportion remained 0.20. Construct a 90% confidence interval for the proportion let go.
4. What is the interpretation of that interval?

You wish to test to see if the proportion in your company is different from that of the economy at large,

in which

e. f. g. h. i. j.

k.

the proportion is 0.15.

What are the appropriate hypotheses?

What is the rejection region?

What is the STS?

If you use the data you already have, what is the p-value? What is your conclusion?

At what level of significance would you be able to conclude that your company proportion is different from 0.15?

Assume you want that level of significance to be 5%. What sample size would you require, again assuming the same proportion of 0.20 for planning?