3. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving: 160 200 220 230 120 180 140 130 170 190 80 120 100 170 a. Make a 95% confidence interval for the average calorie content of vanilla yogurt. Include the sample statistics, degrees of freedom, and standard error. Express the confidence interval in a sentence. b. A diet guide claims that you will get 120 calories from a serving of vanilla yogurt. Based on your confidence interval, is this claim supported? c. What sample size would be needed to obtain a margin of error of 10 calories?

4. According to popcornj.org, the mean consumption of popcorn annually by Americans is 54 quarts. The marketing division of popcorn.org unleashes an aggressive campaign designed to get Americans to consume even more popcorn. a) Determine the null and alternative hypotheses. b) State what a type I error is. c) A sample of 800 Americans provides enough evidence to conclude that the marketing campaign was effective. Suppose, in fact, that the mean annual consumption of popcorn after the marketing campaign is 53.4 quarts. Has a Type I or Type II error been made by the marketing department?