A Frozen Food Company claims that its Healthy Selection frozen TV dinners have no more than 8 grams of fat. A consumer testing agency tested a random sample of twelve such dinners and found that the mean fat content was 14.5 grams, with a standard deviation of 6.5 grams.
a. Construct a 95 percent confidence interval for the true mean grams of fat in the TV dinners.
b. Estimate the minimum sample size necessary to estimate the true mean grams of fat to within plus or minus 2 grams with 98 percent confidence.