Exercises 2.3.7 to 2.3.11 refer to the same study. 2.3.7 According to a 2018 report by the U.S. Department of Labor, ci- vilian Americans spend 2.84 hours per day watching television. A fac- ulty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students. a. Identify the variable of interest and whether the variable is cate- gorical or quantitative. b. Describe Dr. Sameer's parameter of interest and assign an appro- priate symbol to denote it. c. Write the appropriate hypotheses using symbols. 2.3.8 Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television (Exercise 2.3.7). Suppose that Dr. Sameer surveys a random sample of 100 Cal Poly students, and for this sample the mean number of hours per day spent watching TV turns out to be 3.01 hours. a. Is the number 3.01 a parameter or a statistic? b. Assign an appropriate symbol to the number 3.01. c. Describe how you can conduct a simulation-based test of signif- icance to investigate whether the data provide evidence that the av- erage number of hours per day Cal Poly students spend watching TV is different from 2.84 hours. Be sure to provide details on how one would find a p-value. d. For the following table, complete the column on the right to draw parallels between the simulation and the real study: Simulation Real study One repetition = Null model = Statistic = 2.3.9 Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television (Exercise 2.3.7). a. Suppose that on analyzing the data from the survey of a random sample of 100 Cal Poly students, the p-value for Dr. Sameer's study was computed to be 0.16. Interpret what this p-value means in the context of the study. (Hint: This question is not asking for a conclusion from the p-value.) b. Another faculty researcher, Dr. Elliot, had hypothesized that Cal Poly students spend more than 2.84 hours/day watching TV, on average. If Dr. Elliot were to use the same data as Dr. Sameer to conduct an investigation, how, if at all, would this researcher's p-value compare to the p-value reported in (a)? Explain how you are deciding. (Hint: Bigger, smaller, or about the same? If bigger or smaller, by how much?) 2.3.10 Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television (Exercise 2.3.7).Suppose that for the random sample of 100 Cal Poly students the mean number of hours per day spent watching TV turns out to be 3.01 hours, and the standard deviation of the number of hours per day spent watching TV turns out to be 1.97 hours. a. Is the number 1.97 a parameter or a statistic? Assign an appropri- ate symbol to this number. b. Find the standardized statistic to investigate whether the data pro- vide evidence that the average number of hours per day Cal Poly stu- dents Spend watching TV is different from 2.84 hours. 0. What is your conclusion about the hypotheses, based on the calcu- lated value of the standardized statistic? How are you deciding? 2.3.11 Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television (Exercise 2.3.7), and recall that for the random sample of 100 Cal Poly students\" num- ber of hours per day spent watching TV the mean and standard devia- tion turned out to be 3.01 hours and 1.97 hours, respectively. a. In the context of this study, is the theory-based approach (one- sample ttest) valid to nd a p-value to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.84 hours? Explain. b. Regardless of your answer in (a), use the Theory-Based Inference applet to conduct a one-sample t-test to nd and report a standardized statistic (tstatistic) and a p-value for Dr. Sameer's hypotheses. c. State your conclusion from this study based on the p-value report- ed in (b), being sure to provide justication for your conclusion. 2.3.12 A I-distribution looks a lot like a normal distribution, but it is a bit more spread out than a normal distribution with more obser- vations in the \"tails," fewer in the middle. To determine whether a result is out in the tail of a normal distribution, we use a standard- ized statistic of 2 as our guideline. We can use the same guideline for tdistributions. Suppose, however, the standardized statistic of 2 was a precise rule for a normal distribution. Would the corresponding precise rule for a tdistribution use a number that was more or less than 2? Explain