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A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated was 779 for the group that thought about the cheesecake and 1015 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 students in each group, and the standard deviation of the number of calories estimated was 130 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first. Complete parts (a) through (e) below a. State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first. Let μ1 represent the mean number of calories estimated by the people who thought about the cheesecake first and μ2 represent the mean number of calories estimated by the people who thought about the organic fruit salad first. Choose the correct answer below A. H0: μ1 ≥ μ2 B. H0: μ1 ≠ μ2 H1: μ1<μ2 H1: μ1=μ2 C. H0: μ1=μ2 D. H0: μ1 ≤ μ2 H1: μ1 ≠ μ2 H1: μ1>μ2 b. In the context of this study, what is the meaning of a Type I error? A. A Type I error is committed if one concludes that the mean estimate is significantly lower for the people who thought about the cheesecake when it is not significantly lower. B. A Type I error is committed if one concludes that the mean estimate is not significantly lower for the people who thought about the cheesecake when it is significantly lower. C. A Type I error is committed if the alternative hypothesis is rejected but the mean estimate is not significantly lower for the people who thought about the cheesecake. D. A Type I error is committed if the null hypothesis is rejected but the mean estimate is significantly lower for the people who thought about the cheesecake. c. In the context of this study, what is the meaning of a Type II error? A. A Type II error is committed if one concludes that the mean estimate is not significantly lower for the people who thought about the cheesecake when it is significantly lower. B. A Type II error is committed if the null hypothesis is rejected but the mean estimate is not significantly lower for the people who thought about the cheesecake. C. A Type II error is committed if one concludes that the mean estimate is significantly lower for the people who thought about the cheesecake when it is not significantly lower. D. A Type II error is committed if the alternative hypothesis is rejected but the mean estimate is significantly lower for the people who thought about the cheesecake.
Complete parts a-d below. (a) Simplify log8(w^13) + log8(w^5). (b) Solve log8(w^13) + log8(w^5) = 1. (c) Compare the process of simplifying an expression with solving an equation. (d) Explain how simplifying an expression can help when you are solving an equation. (a) log8(w^13) + log8(w^5) = log8(w^18) (b) w ≈ 1.1225 (Type an integer or decimal rounded to four decimal places as needed.) (c) Which of the following is the correct comparison of simplifying an expression and solving an equation? A. Simplifying an expression gives a value that satisfies a given formula, while solving an equation is a process by which complicated logarithmic expressions are reduced. B. Simplifying an expression is a process by which complicated logarithmic expressions are reduced, while solving an equation gives a value that satisfies a given formula. C. Solving an equation is a way to find a value that simplifies an expression to a single logarithm. D. There is no difference. (d) Which of the following explains how simplifying an expression can help when you are solving an equation? A. Simplifying an expression given in an equation will make it easier to put the equation in logarithmic form and solve algebraically. B. Simplifying the expression in a given equation makes it easier to use the properties of logarithms. C. Simplifying an expression does not help when solving an equation. D. Simplifying an expression will help solve an equation because when the expression is fully simplified it can be changed from logarithmic form to exponential form, and then solved algebraically.