Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.

a. i. x - =________ ii. σ =________ iii. n =________

b. In words, define the random variables X and X - .

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean height of male Swedes.

i. State the confidence interval.

ii. Sketch the graph.

e. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?