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STAT 217: STATISTICAL METHODSWINTER 2012Lab #6: Bob and TimDue: 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 #6 (instructions on Moodle). You should use this Word file to take notes and record output as you proceed through the lab. Print out a hard copy of your answers to all 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 simple numerical and graphical summaries comparingtwo groups on a quantitative response - Continue to explore the concept of “statistical significance” and p-values for the scenario of comparing two groups on a quantitative variable- Obtain and interpret a confidence interval for the difference in two population means- Use the results of a designed experiment and sample data to draw conclusions about a populationSymbols for possible use: , -, pˆ, -, -, sData Collection(a) In your report (now or later) write a paragraph (not just a listing of terms) summarizing how the data were collected for this study. Be sure to include in context (you may also want to review the details given on page 1 of the online lab instructions):- Observational units- Explanatory and response variables (be sure to classify as categorical or quantitative),- Identify with justification the type of study (anecdotal, observational, or experimental),- Describe the type(s) of randomness used (random assignment and/or random sampling),- Describe the sample used in the study,- State the sample size, including the number of individuals in each treatment group.>> Descriptive Statistics and Discussion(b) Use JMP to produce a graphical summary comparing the responses (improvement scores) of the two treatment groups. (Note: A negative improvement score indicates the subject did worse on the second testing.) Make sure to include a meaningful title and clearly label the two groups.Copy/paste your stacked histograms (with uniform scaling modified titles) here.1(c) Compare the distributions of the improvement scores (as best you can with so few observations) between these two groups. (Make sure you discuss (supporting with appropriate statistics) shape, center, spread, outliers and other unusual observations. There may not be an obvious overall pattern but give your reader a sense of the visual images you are looking at. Also include the sample sizes. Everything should be written in the context of this study.)>> (d) Also address the following questions:- Report the observed difference in the mean improvement scores for the two treatment groups (deprived - unrestricted). >> - Is this difference a statistic or parameter? Explain. >> - Explain what it means that the difference in means is negative. >> - Does this difference seem small or large to you? What does this difference suggest about the effects of depriving sleep? Does it appear that subjects who "caught up" on sleep were able to perform as well as subjects getting unrestricted sleep on this visual discrimination task? >> - Conjecture whether you expect this difference will turn out to be “statistically significant” and state why or why not. >> Statistical Inference(e) NULL HYPOTHESIS and ALTERNATIVE HYPOTHESIS: State, in symbols, your null and alternative hypotheses for this study. Clearly define in words the symbols you are using, in the contextof this study. (Hint: Make sure it is clear that these are parameters, not populations or statistics.)>> Simulation – 1000 repetitions under the null hypothesis (f) Create a randomization distribution of 1000 repetitions of the random assignment process.Paste screen capture from applet here.(g) Summarize what you have learned from the simulation- Make sure you clearly explain what this simulation represents.- What are the observational units and variable of this new dotplot?- Describe the shape, center, and spread (with appropriate numerical support) of this distribution.- This distribution should center around zero, why? Explain.2- Where does the difference in group means (deprived group - unrestricted group) observed by these researchers fall in this graph (near the middle or in a tail) Is it a surprising outcome? Enough for you to reject the null hypothesis? How are you deciding? - Interpret the p-value in your own words: If we repeatedly…. (Don't simply decide whether it's small, but explain what it measures: The proportion of whats that do what assuming what?).>> Theoretical Result(h) Do you believe the technical conditions for this result are met for this study? Explain.>> (i) Reconsider the randomization distribution you generated in part (f). Is the mean of the randomization distribution close to the hypothesized difference in population means? Is the standard deviation of the randomization distribution close to 5.93?>> Using the t-distribution to model the randomization distribution under the null hypothesis:Paste JMP output here.(j) Find and report the appropriate p-value for our alternative hypothesis.>> (k) What conclusion would you draw from this p-value? How does this p-value compare to the one you found with the simulation?>> (l) Find and report the confidence interval for our parameter. Write a one-sentence interpretation of this interval. (Hint: What is the parameter?)>> Conclusions(m) Summarize your conclusions as if to the readers of a popular science journal including whether the observed difference is considered statistically significant (with justification), whether you are drawing a cause and effect conclusion, and to what population (justify these last two claims based on how the data were collected and the significance of the results), and any potential problems with the study and how it could be improved if you were to conduct it in the future. >> Application3(a) Open the FakeSleepDeprivation.jmp data file. Reproduce the graphical and numerical summaries as before. How do these data compare to the actual study data (e.g., shape, center, spread)?Paste JMP output here.>> (b) Using the same null and alternative hypotheses, conjecture how the statistical significance of these data will compare to that of the actual study data (e.g., larger p-value, smaller p-value, same p-value). Briefly explain your reasoning.>> (c) Carry out the two-sample t-test and obtain the p-value. How does the test statistic compare (larger, smaller,


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Cal Poly STAT 217 - lab 6

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