STAT 217: STATISTICAL METHODSWINTER 2012Lab #1: Bob and TimDue: Beginning of classThursday, Jan 13 (section 3)Friday, Jan 14 (sections 1, 2)No late work will be accepted!Directions: Working in pairs, work through Lab #1 (instructions on Moodle). You should use this Word file to take notes and record output as you proceed through the lab. What you are to submit and what will be graded is only the Application questions. Print out a hard copy of those questions, fold your report lengthwise, and put your names on the outside of the report, along with your section number.Goals for this lab:- Investigate a research question through:o Simple numerical and graphical summaries o Use of a coin tossing applet - Explore the concept of “statistical significance” and p-values to assess a research conjecture- Use sample data to draw conclusions about a populationDescriptive Statistics(a) What are the observation units and variable for these data? [Hint: Remember to state the variable as a question that could be asked of each individual observational unit.]>> (b) Report both the number of students and the percentage of students from the class data who identified the face on the left as Tim. Also, report the sample proportion (a number between 0 and 1, using 3 decimal places).Count Percentage Proportion BobTimCopy and paste your bar chart of the sample data from JMP or Excel here. Make sure the axes are well labeled (y-axis should be a percentage) and the graph has a meaningful title. Discussion(c) Based on your numerical and graphical summaries from above, write a few sentences summarizing the results for this sample. For example: What did you learn about the tendency for yourclass to identify the left picture as "Tim"? Was there a majority (more than 50%) or a pretty equal split? Did the size of the majority surprise you? Also describe the sample for which these results weretaken (e.g., who was involved in this study), including the sample size.1>> The Simulation – 1000 repetitions under the null hypothesis (chance alone model)(d) You want to keep the probability of heads set to .5. Why?>> (e) What do you need to change the number of tosses to? Why?>> (f) How many heads did you get in your first repetition? What proportion of heads did you get in your first repetition? If you repeat this process many, many times, will you always get this same proportion of heads? Explain.>> (g) What are the observational units and variable in this dotplot? [Hints: You should give different answers from question (a)! What do you have to do to add another dot to the dotplot? This is your observational unit...] >> The previous question is important. Ask the instructor or TA if you are not sure.(h) What are the most common outcomes for “proportion of heads” in your dotplot? Why is the dotplotcentered at 0.5?>> (i) Paste the screen capture of your applet results here.Analysis(j) The simulation is carried out under the assumption that students are choosing equally between Bob and Tim for the picture on the left. Based on your simulation results, what proportion of the 1000 repetitions of the study resulted in a proportion of at least as large as the class proportion that chose Tim on the left? >> 2(k) Fill in the blanks in the following sentence to interpret the proportion from part (j).Under the assumption that _______________ if we repeated the process of asking this many students to pick a name for the face on the left many, many times, we would get results as extreme or more extreme than _______, in about __________% of the repetitions.The previous question is important. Ask the instructor or TA if you are not sure.Conclusions(l) Under the assumption that people choose equally between the two names, is it plausible (believable, credible) that the class results from yesterday happened just by random chance? Cite (again) what you found for the class results and then explain using the p-value you approximated withthe applet.>> (m) So if you were publishing these results in a research article, would you say these data provide convincing evidence that the probability a Stat 217 student names the left picture Tim is larger than 0.50? Explain. >> (n) Are you willing to generalize this conclusion to a larger population as well? What population do you think your class is representative of with respect to this research question?>> Application – Can Chimpanzees Solve Problems?(a) Identify the observational units and variable in this study.>> (b) Create numerical and graphical summaries of the sample results (by hand or with Minitab). Include output hereSummarize what these graphical and numerical summaries reveal.>> 3(c) Translate the research question into a research conjecture that we can test. What will be the assumption underlying the null distribution?>> (d) Use the Coin Tossing applet to estimate the p-value for these results. Include a screen capture of the applet displaying the inputs and the proportion of repetitions output. Include output hereUse the "sample proportion" scale and explain why the dotplot is centered where it is.>> (e) Provide a detailed interpretation of the p-value you found, as in question (k), in this context.>> (f) Summarize the conclusions you would draw from this study. Do you think Sarah got lucky or do you think something other than random chance was at play? Be sure to justify your answer statistically! What population are you willing to generalize these results to?>> Before Turning in Your Lab Report:- Proofread!!!!!!!!!- Staple your pages together. Reports that are not stapled will not be graded!- Fold the report in half (lengthwise). Put both team members names (first and last names) on the outside of the report with your section