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Weights of diamonds are measured in carats 1 carat = 100 points, 0.99 carats = 99 points, etc. The difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the naked human eye, but does the price of a 1 carat diamond tend to be higher than the price of a 0.99 diamond? We are going to test to see if there is a difference between the average prices of 0.99 and 1 carat diamonds In order to be able to compare equivalent units, we divide the prices of 0.99 carat diamonds by 99 and 1 carat diamonds by 100, and compare the average point p 0.99 carat pt99 1 carat X 53.43 s 1 2.22 n 30 1- Which of the following is the correct set of hypotheses for testing if the average point price of 1 carat diamonds (pthO) is higher than the average point price of 0.99 carat diamonds (pt99)? A- H0 : ppt99 : \"puoo HA 1 \"W99 5E nuptloo 13' Ha: \"13:99 = \"moo 2- Which of the following does n_0t need to be satised in order to conduct this hypothesis test using theoretical methods? A. Point price of one 0.99 carat diamond in the sample should be independent of another, and the point price of one 1 carat diamond should independent of another as well B. Point prices of 0.99 carat and 1 carat diamonds in the sample should be independent. C. Distributions of point prices of 0.99 and 1 carat diamonds should not be extremely skewed D. Both sample sizes should be at least 30 3- Which of the following does n_ot need to be satised in order to conduct this hypothesis test using theoretical methods? A. Point price of one 0.99 carat diamond in the sample should be independent of another, and the point price of one 1 carat diamond should independent of another as well B. Point prices of 0.99 carat and 1 carat diamonds in the sample should be independent. C. Distributions of point prices of 0.99 and 1 carat diamonds should not be extremely skewed D. Both sample sizes should be at least 30