Before now, we have mostly applied the chance model to situations where the observational units are attempts by a single individual (e.g., Buzz the dolphin, Sarah the chimp, Phil the golfer). In this investigation you applied the same chance model to a situation where there is a single attempt by each of a set of individuals. This means that the chance model is not only assuming that each attempt has the same chance of success, but that each individual has the same chance of success. While testing this chance model uses the same simulation strategy we have seen before, when we find evidence the chance model is wrong this only means that we have evidence that all individuals are not employing a random chance model. What we don’t know is whether only some or all of the individuals are applying a non-random chance model when making attempts.Often in Statistics, chance models are applied to complex situations. It is important to recognize the assumptions of chance models to ensure that we are not assuming too much about the conclusions that can be drawn from a study. One key question that is often asked is about generalizability of the conclusions to a larger group. For example, if there’s evidence that these 16 infants are not randomly choosing, would you expect to see similar behavior in another set of 16 infants? In other words, does our conclusion about these 16 infants apply or generalize to a larger set of infants? Does your class’s tendency to pick the right front reflect a tendency for all students at your school? All students nationally in your age group? This issue of generalizability is a critically important question that motivates most of our investigations in the next chapter.Winter, 2012 Thursday, Jan. 12Stat 217 – Day 7Reminders:- No class meeting Monday- We will meet in the library on Tuesday - You should complete the prelab for Lab 2 before 9am on Tuesday. You will only have one attempt on the pre-lab this week.- You should complete quiz 2 in Moodle before 9am on Tuesday.- I added a practice problem for this week (“statistical inference”) to PolyLearnInvestigation 2: Which Tire? (Due Tuesday Jan. 17) Please work with a partner and submit one report with both names. A legendary story on college campuses concerns two students who miss a chemistry exam because of excessive partying but blame their absence on a flat tire. The professor allowed them to take a make-up exam, and he sent them to separate rooms to take it. The first question, worth five points, was quite easy. The second question, worth ninety-five points, asked: Which tire was it? Yesterday we collected data from you, asking which of the four tires you would pick if you werecaught in this situation (and had to make up a tire on the spot). You will use these data to conduct a test of whether the sample data support the conjecture that the right front tire is picked more often than we would expect if the four tires were picked equally often (purely at random).Step 1: Ask a research question(a) Identify the research conjecture. >> Step 2: Design a study (b) What are the observational units?>> (c) What is the variable that is measured/recorded on each observational unit?>> (d) Because I want to focus on the right front tire, the parameter of interest in this study is the probability that a Cal Poly student picks the right front. What symbol should I use to refer to this unknown value: pˆ, , , , , s – copy and paste below.>> (e) Based on our research conjecture, state the appropriate null and alternative hypotheses to be tested. (Write these out both in words and using symbols.)>>Winter, 2012 Thursday, Jan. 12Step 3: Collect data(f) Give some information about the sample of individuals that responded to the survey. (A one sentence description is fine.)>> Step 4: Explore the dataOpen the file FlatTire.jmp from the lecture notes page and create a bar graph and summary table. Include a screen capture of your output.(g) What proportion of students selected the right front tire? How many students participated? (Include the symbols you would use to represent these values.)>> Step 5: Draw inferences(h) Is the sample proportion who selected the right front tire greater than one-fourth? (If not, there’s no need to conduct a simulation analysis. You will have no evidence that this tire is selected more than one-fourth of the time in the long run.)>> (i) If we assume that each student is randomly selecting among the four tires, what is the probability that an individual will select the right front tire? >> (j) Use the Simulation-Based One-Proportion Inference applet to simulate 1000 repetitions of this study, assuming that every student in class selects randomly among the four tires. Also determine the approximate p-value from your simulation analysis. Include a screen capture of your applet output, make sure it’s clear what values you input into the applet and that the p-value results are displayed.>> (k) What is the center of your simulated null distribution? Does it make sense that this is the center? Explain.>> (l) Based on the dotplot generated using the 1000 “could have been” values of the statistic, what values would you consider typical values and what would you consider atypical values of the statistic when the chance model (null hypothesis) is true?>>Winter, 2012 Thursday, Jan. 12 (m) Interpret what this p-value represents (i.e., the probability of what, assuming what?).>> (n) Based on using .05 as the level of significance, would you reject or fail to reject the null hypothesis?>> Step 6: Formulate conclusions(o) Summarize the conclusion that you draw from this study and your simulation analysis. Alsoexplain the reasoning process behind your conclusion. [Make sure you tie this back to the p-value!]>> Step 7: Communicate Findings(p) Now, let’s step back a bit and think about the scope of our inference. What are the wider implications? Do you think that your conclusion holds true for people in general? (These are extremely important questions, that we’ll discuss more when we talk about the scope of inference in Chapter 2.)>> SummaryBefore now, we have mostly applied the chance model to situations where the observational units are attempts by a single individual (e.g., Buzz the dolphin, Sarah the chimp, Phil the golfer). In this investigation you applied the same chance model to a situation where there is a single attempt by each of a set of individuals. This means that