B. C. Short Answer: Show ALL WORK and state your answers as complete sentences 1. (30 points) A fitness instructor wants to understand the relationship between her heart rate (in beats per minute) during a workout and the number of calories burned per minute during the workout. She recorded these two measurements over the course of several workouts, and the results are contained in the Statcrunch Analyses for Problem 1. A. What are the predictor and response variables in this situation? Fully interpret the scatterplot relating heart rate and the number of calories burned per minute during the workout. Is there a relationship between the heart rate during a workout and the calories burned per minute? Use a = 0.05. Identify the regression equation for this situation and interpret the slope coefficient for this model in the context of the situation. E What percentage of the total variation in the number of calories bumed is explained by the regression model? F. If appropriate, estimate of the number of calories burned per minute when the instructor's heart rate is 100 beats per minute. If it's not appropriate, explain why not If appropriate, estimate of the number of calories burned per minute when the instructor's heart rate is 150 beats per minute. If it's not appropriate, explain why. If appropriate, estimate the mean number of calories burned per minute during all workouts for which the instructor's heart rate is 150 beats per minute. Use 95% confidence. If it's not appropriate, explain why. D. G H 2. A (24 points) A large, public university wants to determine if a majority of its students use iPhones. The university randomly selects 122 of its students and asks each student whether or not they use an iPhone. Eighty (80) of these 122 students use an iPhone. What is the population for this study? B. What is the sample for this study? C. What is the variable of interest for this study? D. Do the data provide evidence that more than 50% of all students at the university carry an iPhone? Use a = 0.05. E Is the procedure used in part D valid? Justify your answer in the context of the problem. F. How many students should be selected to estimate the proportion of students that use an iphone with 95% confidence and within a margin of error of 2%? Note that you may use the data presented in the problem as an initial (pilot) estimate of this proportion. (16 points) To test the claims of herbal companies, the National Institutes of Health (NIH) conducted a study to determine the impact of gingko biloba on memory. A representative sample of 208 individuals participate in the study and are randomly assigned to one of two groups: (Group 1) the Gingko group, who supplement their diet for 60 days with Gingko tablets, and (Group 2) the Control group, who receive a placebo for 60 days. Based upon pre-tests, the entering memory levels of the two groups are approximately equal. At the end of the 60 days, each group then completes a standardized memory test and their scores are recorded. A Are the scores on the standardized memory test of the 104 Gingko participants and 104 Control participants, independent or dependent samples? Explain. B Using the appropriate table from the StatCrunch Analyses for Problem 3, determine whether there is evidence that, on average, the mean memory test scores of all individuals receiving Gingko (Group 1) supplements exceeds those of all individuals receiving no Gingko (Group 2). Use a = 0.05. C. Physicians will prescribe gingko, an expensive drug, if they have evidence that it improves memory. Describe a Type I error, in the context of this problem. D. Discuss the consequences of a Type I error, in the context of this problem. 3. StatCrunch Analyses for Problem 1 Cals burned per minute 8.5 8 7.54 6.5 135 140 155 160 145 150 Avg, H.R. Simple linear regression results: Cals burned per minute - -1.7339468 +0.061427752 Avg. H.R. Sample size: 46 R (correlation coefficient) = 0.72711706 Estimate of error standard deviation: 0.41345617 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -1.7339468 1.2983143 70 44 -1.335537 0.1886 Slope 0.061427752 0.0087434539 +0 44 7.0255705