A rancher would like to estimate the average weight pain of the cattle is his herd between the time of purchase and the time he takes them to market. If he selects a sample of size n = 16 animals and finds x-bar = 240 lbs and s = 32 lbs, construct a 95% confidence interval for the true average weight gain per animal. Assume weight gain is normally distributed.

2. An insurance company surveys 25 households at random and finds that the average amount of whole life insurance owned by these 25 households is $60,000 with a standard deviation of $20,000. Assume that the amount of whole life insurance is normally distributed. Find a 95% confidence interval for the true average amount of whole life insurance per household. Interpret your result. Was the assumption of normality necessary? Why or why not?

3. An advertising company wishes to estimate the true average amount of TV viewing time per household. Suppose it wants to estimate the true average viewing time within ±10 minutes and be 99% confident that this is a correct estimate. How many households will have to be part of the sample they select? You may assume that a previous year's sample had a standard deviation of s = 45 minutes.

4. The manufacturer of a small twin-engine jet airplane is concerned about the difference between the thrusts produced by the port (left) and starboard (right) engines. Sixteen aircraft were tested, and the difference between the port and starboard thrusts (in pounds) was recorded for each case as shown here.

-60 30 120 80 -110 20 130 -50

50 -90 40 -70 -90 100 -80 20

Assuming that thrust differences are approximately normally distributed, find a 90% confidence interval for the true average difference between engine thrusts.