1. At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, "You can average more than $20 a day in tips." Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $24,85, with a standard deviation of $3.24. Can Ms. Brigden be 99% confident that she is earning an average of more than $20 per day in tips?
2. The Gibbs Baby Food Company wants to compare the weight gain of infants using their brand versus their competitor's. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babies using the competitor's brand revealed a mean increase in weight of 8.1 pounds in the first three months after birth, with a standard deviation of 2.9 pounds. Can Gibbs be 95% certain that babies using their products gained less weight?
3. Stargell Research Associates conducted a study of the radio listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes per day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. Can Stargell be 90% certain that there is a difference in the variability of the listening times for men and women?
4. Shank's, Inc., a nationwide advertising firm, wants to know whether the size of an advertisement and the color of the advertisement make a difference in the response of magazine readers. A random sample of readers is shown ads of four different colors and three different sizes. Each reader is asked to give the particular combination of size and color a rating between 1 and 10. Assume that the ratings are approximately normally distributed. The rating for each combination is shown in the table following (for example, the rating for a small red ad is 2). Is there a difference in the effectiveness of an advertisement by color and by size? Use the 0.05 level of significance.
Color of Ad
Size of Ad Red Blue Orange Green
Small 2 3 3 6
Medium 3 5 6 7
Large 6 7 8 8