Based on a sample of 33 different electric car models, I have calculated two confidence intervals for the mean number of miles the cars can travel on a single full charge. The first is (238 miles, 260 miles). The second is (240 miles, 258 miles).

a. Based on the above information, what was the value of the sample mean? _____________

b. What is the margin of error for the (238 miles, 260 miles) interval? ________________

c. What is the margin of error for the (240 miles, 258 miles) interval? ________________

d. One of the intervals is the 95% Confidence Interval while the other is the 90% Confidence Interval. Which interval is the 95% Confidence Interval? ________________

e. If the sample size had been 50 electric cars instead of 33 electric cars, how would this have altered the width of these confidence intervals?

f. How large of a sample is needed at the 95% Confidence Level if we want the margin of error to be 6 miles? Assume = 30 miles. Show work.

g. Use n = 40, = 250, and = 25 to construct a new 95% Confidence Interval for the mean number of miles an electric car can travel on one charge. Do this "by hand" using the formula from class. You may of course check your answer using the z-interval feature on your calculator.

h. Explain the meaning of the 95% Confidence Interval you just calculated.