1) Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the = 0.05 level of significance?

Diet A	5	8	7	9	11	7	14	6	12	6
Diet B	22	11	22	7	9	6	14	21	14	6

Find t. (Give your answer correct to two decimal places.) Find the p-value. (Give your answer correct to four decimal places.)

2) If a random sample of 28 homes south of a town has a mean selling price of $145,000 and a standard deviation of $4825, and a random sample of 15 homes north of a town has a mean selling price of $148,425 and a standard deviation of $5675, can you conclude that there is a significant difference between the selling price of homes in these two areas of the town at the 0.05 level? Assume normality. Find t. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) 3) Consider the following.(a) Calculate the estimate for the standard error of difference between two independent means for s₁² = 14, s₂² = 14, n₁ = 16, and n₂ = 19. (Give your answer correct to two decimal places.) Calculate the estimate for the standard error of difference between two independent means for s₁² = 0.061, s₂² = 0.088, n₁ = 8, and n₂ = 9. (Give your answer correct to four decimal places.) Calculate the estimate for the standard error of difference between two independent means for s₁ = 3.2, s₂ = 6.5, n₁ = 15, and n₂ = 30. (Give your answer correct to two decimal places.)

4) Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie cheese. She randomly samples 12 wheels of Gouda and finds the mean is 0.9 lb with a standard deviation of 0.37 lb; she then randomly samples 18 wheels of Brie and finds a mean of 0.97 lb and a standard deviation of 0.3 lb. What is the p-value for Heidi's hypothesis of equality? Assume normality. (Give your answer correct to four decimal places.)