Question 1.

a) If you were constructing a 95% confidence interval of the population mean based on a sample of n=60 where the standard deviation of the sample s = 0.06, what is the critical value of t that you should use? Explain/show how you obtain your answer. (7 pts.)

b) In your question above, what is your margin of error?  What would it be if you were constructing a 99% confidence interval? (7 pts.)

c) Consider the following two scenarios. (A) The simple random sample of 60 was taken from sophomore undergraduate students at your college. If the simple random sample of 60 was taken from a general population of young women instead, would you expect s to be the same? Which sample should have the smaller margin of error? Explain your answer. (6 pts.)

Question 2. You want to know how the commuting time of your employees compare to Departments competing for the same staff, so you get some survey data on average commuting times for 25 randomly selected people in your line of business.

Data: 59, 74, 73, 66, 80, 84, 90, 122.5, 37.2, 50, 139.3, 39, 80, 35, 88, 34, 82, 65, 61, 63, 66, 88, 70, 79, 75

You find that the mean commuting time is 72 minutes, with a standard deviation of 24.53. (Check for yourself!)

a) Calculate your standard error. (3 pts.)

b) Based on this, calculate a 95 percent Confidence Interval for the mean commuting time. (Remember, the C.I. is calculated by adding and subtracting from the observed sample mean the product of the standard error and the appropriate t-value; for the latter, you may use Excel tinv) Show your work. (7 pts.)

b) Given the data in the question above about mean commuting time, calculate the 90% Confidence Interval. (Again, show your work. (5 pts.)

c) Which is a bigger range, the 95% or 90% confidence interval? Why? (3 pts.)

d) What assumptions must you make about the population when constructing confidence interval estimates? (2 pts.)