Winter, 2012STAT 217: STATISTICAL METHODSWINTER 2012Lab #5: Sleepless NightsDue: Beginning of classThursday, Feb. 16 (section 3)Friday, Feb. 17 (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. You are to submit the entire lab report. 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:To analyze a quantitative response variable using numerical and graphical summaries and using one-sample t-procedures to make inferences about a population mean, considering several possible population shapes.Symbols for possible use: , , , , , sDescriptive Statistics: (a) Produce numerical and graphical summaries of our sample data. [Make sure your graph has a titleand/or axis label.]Paste a copy of your output here.(b) Write a paragraph summarizing the distribution of sleep time responses in this sample. (Make sure you discuss (with supporting evidence) shape, center, spread (using appropriate symbols), and outliers. Also, report the sample size and make sure your comments are in context.) >> Then:Does the distribution behave as you expected in the prelab? >> Do the data support the research conjecture that Cal Poly students average less than 8 hours of sleep on a typical Sunday night?>> Population Model: (c) Do we know the value of the population mean amount of sleep on a typical Sunday night for all Cal Poly students? What symbol can we use to represent its value?>> 1Winter, 2012(d) Translate the above statement (online) to null and alternative hypothesis statements (Ho and Ha) (write out hypotheses in both symbols and in words).>> (e) Do we know the value of the population standard deviation? What symbol can we use to represents its value? Provide a one-sentence interpretation of what this value would represent in this context. >> Population Model/ Central Limit Theorem: Population ShapeNormal (f) Right skewed (h) Left skewed (i) Very right skewed(j)Paste (and shrink) screen capture herePaste screen capture herePaste screen capture herePaste screen capture hereShapeMeanStd. DeviationApprox p-value(g) Why did we count below instead of above?>> (k) Did the assumed shape of the population distribution of sleep times make a substantial difference in the approximate p-value? Explain. >> (l) Calculate the standard error for our class data. >> (m) Use the standard error to standardize the observed sample mean compared to the population mean: (observation - mean)/standard error>> Statistical Inference:2Winter, 2012Paste screen capture here.(n) Provide an interpretation of the "test statistic" provided in the output.>> (o) Provide an interpretation of this p-value in this context. Hint: The proportion of random samples that... assuming .... >> (p) Based on this p-value (and the standard cut-off values from Lab 1), will you reject or fail to reject the null hypothesis? >> (q) Provide a one sentence interpretation of the confidence interval. Hint: What is supposed to be in the interval?>> Application:(r) Now repeat the analysis to test the research conjecture that that the average amount of sleep by all Cal Poly students Sunday night differed from 7 hours.Paste a copy of your output here.>> (s) Now reconsider your confidence interval for the population mean from before (question q). Based on this interval, could you have predicted how this test of significance would have turned out? Explain.>> (t) What does the confidence interval tell you about how Cal Poly students compare to the website's claim in the pre-lab that college students average 6-6.9 hours of sleep a night? >> Summary:3Winter, 2012(u) Summarize (in a paragraph) what you have learned in this lab about the sleep habits on a typical night of all Cal Poly students. (There will be some repetition from what you have said earlier.) If you have any concerns about the “technical conditions” of the analysis procedures we used, state them now. In particular, Validity: Do you consider the conditions necessary for the Central Limit Theorem to have been met? Explain. Significance: Is 8 a plausible value for the average amount of sleep on a typical Sunday night by all Cal Poly students? Estimation (confidence): What are plausible values? How do Cal Poly students compare to the 6-6.9 hours averaged by college students overall? Generalizability: Any concerns about generalizing our sample results to the larger population of all Cal Poly students?>> 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
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