**How are these done using Excel? **

1. Consider a finite population with 5 elements

labeled A, B, C, D and E. 10 possible simple random samples of size 2 can be selected.

a. List the 10 samples beginning with AB, AC, and so on.

b. Using simple random sampling, what is the probability that each sample of size 2 is selected?

2. In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined.

a. Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean for the following.

b. With a 0.95 probability, determine the margin of error.

c. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?

3. A researcher is testing a new painkiller that claims to relieve pain in less than 15 minutes, on average. What’s would be the hypotheses associated with the researcher’s test.

4. At a certain manufacturing plant, a machine produced ball bearings that should have a diameter of 0.50 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 30 ball bearings to test to see if the process is “out of control” (i.e. to test to see if the average diameter differs from 0.50 mm).

a. State the hypotheses associated with the manager’s test.

b. Describe a Type I error for this situation.

c. Describe a Type II error for this situation.