4 questions-The following table shows different baskets of black pens:

1. The following table shows different baskets of black pens:

baskets number of baseballs population

1 10

2 18

3 7

4 11

5 6

(a) List all samples of size 2, and compute the mean of each sample.

(b) Compute the mean of the distribution of the sample mean and the population mean. Compare the two values.

(c) Compare the dispersion in the population with that of the sample mean.

2. The NJ Department of Transportation conducted a study to find the average amount of time car drivers spend commuting during weekends. They surveyed 196 car drivers and the study found out that the driver’s population spent an average of 13 hours commuting with a standard deviation of 11 hours.

(a) What is the standard error of the mean?

(b) Compute the probability the sample mean is greater than 15 hours?

(c) Compute the probability the sample mean is less than 13 hours?

(d) Compute the probability the sample mean is between 13 and 17 hours?

3. NC State University conducted a study to see how many students attended a women’s baseball game last season. There are 33,500 students attending NC State University, and the study showed that 450 of 950 students sampled attended a women’s soccer game. What inferences can be made about student attendance at women’s soccer games?

(a) What is the estimated proportion for the population?

(b) Using the 95% level of confidence, what is the confidence interval?

(c) Using the 99% level of confidence, what is the confidence interval?

4. The department of HR at the University of Michigan wants to estimate the amount of an annual healthcare premium needed for an Assistant Professor as part of a new recruiting program. In a sample of 50 Assistant Professors, they found that the average yearly premium needed is $16,000 with a standard deviation of $3,500.

(a) What is the population mean? What is the best estimate of the population mean?

(b) Develop an 90% confidence interval for the population mean.

(c) Assuming a 99% level of confidence, how large of a sample is required with an acceptable error of $400?