1. A biologist claims that the mean cholesterol content of chicken eggs can be reduced by giving a special diet to chickens. When thirty-six eggs obtained in this way were tested, it found out that the cholesterol content was 260 mg with a sample standard deviation equal to 22 mg. is the true mean cholesterol content significantly less than 280 mg? Use a = 0.0513. From his long standing experience, a farmer believes that the mean yield of grain per plot in his farm is 160 bushels. When a new seed introduced on the market was tried on sixteen randomly selected experimental plots, the mean yield was 168 bushels. Suppose the yield per plot can be assumed to be normally distributed with a standard deviation of yield of 22 bushels. Is the new seed signicantly better? Use a = 0.05 4. The label on a can of pineapple slices states that the mean carbohydrate content per serving of canned pineapple is over 55 grams. It may be assumed that the standard deviation of the carbohydrates content is 4 grams. A random sample of twenty-five servings has a mean carbohydrate content of 57.3 grams. Is the company correct in its claim? Use a = 0.05 5. A company has two branches, one on the East Coast and the other on the West Coast. The mean daily sales of the company on the East Coast, when observed on 100 days, were found to be P250,000 with $1=P35,000. For the company on West Coast, when observed on 200 days, the mean daily sales were P245,000 with S2=P25,000. At the 5 percent level of significance, do the two branches differ in their true mean daily sales? (Assume that the sales in the two branches are normally distributed). 6. A ski coach claims that she can train beginning skiers for 3 weeks so that at the end of the program they will finish a certain downhill course in less than 15 minutes. It was found that, when a random sample of ten skiers given the training, their mean time was 14.1 minutes with standard deviation of 1.4 minutes. On the basis of the evidence, is the true mean significantly less than 13.5 minutes? Use a = 0.025