Is a weight loss program based on exercise just as effective as a program based on diet? The 52 overweight people put on a strict one year exercise program lost an average of 27 pounds with a standard deviation of 10 pounds. The 48 overweight people put on a strict one year diet lost an average of 21 pounds with a standard deviation of 8 pounds. What can be concluded at the a = 0.01 level of significance?

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.7 and a standard deviation of 23.1. Use a 0.01 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Traffic Highway planners investigated the relationshipbetween traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately largecity thoroughfare. The data were collected at the samelocation at 10 different times over a span of 3 months.They found a mean traffic Density of 68.6 cars per mile(cpm) with standard deviation of 27.07 cpm. Overall, the cars’ average Speed was 26.38 mph, with standard devia-tion of 9.68 mph. These researchers found the regression line for these data to be Speed = 50.55 - 0.352 Density.a) What is the value of the correlation coefficientbetween Speed and Density?b) What percent of the variation in average Speed isexplained by traffic Density? c) Predict the average Speed of traffic on the thorough-fare when the traffic Density is 50 cpm. d) What is the value of the residual for a traffic Densityof 56 cpm with an observed Speed of 32.5 mph?e) The data set initially included the point Density =125 cpm, Speed = 55 mph. This…

Low-fat or low-carb? Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.7 kilograms with a sample standard deviation of 7.16 kilograms. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kilograms with a standard deviation of 5.90 kilograms. Can you conclude that the mean weight loss differs between the two diets? Let 4, denote the mean weight lost on the low-carb diet and u, denote the mean weight lost on the low-fat diet. Use the a = 0.01 level and the TI-84 Plus calculator. Compute the -value. Round the answer to four decimal places. Determine whether to reject H0 State a conclusion