ࡱ> [ zbjbj77 4|U\U\5 """"T"Ur___RTTTTTTTTTTTTT$XZxTQ_____xTT)")")"_ RT)"_RT)")"JVO(Ei.M*>TT0UXMY[Y[TVOVOY[RD__)"_____xTxT ___U____Y[_________ > : Stat 1350 Elementary Statistics Jigsaw Review for Test 2 Chapters 14-15 and 17-20 Group 1 Regression - Chapters 14-15: 1. From Rex Boggs in Australia comes an unusual data set: before showering in the morning, he weighed the bar of soap in his shower stall. The weight goes down as the soap is used. The data appear in Table II.3 (weights in grams). Notice that Mr. Boggs forgot to weigh the soap on some days.  HYPERLINK "JavaScript:top.OpenSupp('table',26,3)"  INCLUDEPICTURE "http://ebooks.bfwpub.com/scc7e/tables/26_T_3.gif" \* MERGEFORMATINET  Plot the weight of the bar of soap against day.   Is the overall pattern roughly straight-line? Based on your  HYPERLINK "JavaScript:top.Define('scatterplot')" scatterplot, is the  HYPERLINK "JavaScript:top.Define('correlation')" correlation between day and weight close to 1, positive but not close to 1, close to 0, negative but not close to "1, or close to "1? Explain your answer. The overall pattern is roughly straight-line. The correlation would be close to -1 since the points are very close to lying on a straight decreasing line. Find the equation for the  HYPERLINK "JavaScript:top.Define('leastsquaresregressionline')" least-squares regression line for the data in Table II.3 and write it below. Draw the  HYPERLINK "JavaScript:top.Define('regressionline')" regression line on your  HYPERLINK "JavaScript:top.Define('scatterplot')" scatterplot from the previous exercise. y = 133.18 6.31x Explain carefully what the  HYPERLINK "JavaScript:top.Define('slope')" slope b = "6.31 tells us about how fast the soap lost weight. Every day the weight of the soap decreases 6.31 grams. Mr. Boggs did not measure the weight of the soap on Day 4. Use the regression equation to predict that weight. y = 133.18  6.31(4) = 107.94 grams Use the regression equation in the previous exercise to predict the weight of the soap after 30 days. Why is it clear that your answer makes no sense? Whats wrong with using the  HYPERLINK "JavaScript:top.Define('regressionline')" regression line to predict weight after 30 days? After 30 days the soap would weigh 56.12 grams which is physically impossible. Extrapolation is risky!!! Group 2 Probability Chapters 17-20 1 Choose a student at random from all who took Stats 1350 in recent years. The  HYPERLINK "JavaScript:top.Define('probability')" probabilities for the students grade are  INCLUDEPICTURE "http://ebooks.bfwpub.com/scc7e/tables/31_T_UN_1.gif" \* MERGEFORMATINET  What must be the  HYPERLINK "JavaScript:top.Define('probability')" probability of getting an F? What is the probability that a student will fail the class (earn D or F)? If you choose 5 students at random from all those who have taken Stats 1350, what is the  HYPERLINK "JavaScript:top.Define('probability')" probability that all the students chosen got a B or better? To simulate the grades of randomly chosen students, how would you assign digits to represent the five possible outcomes listed? Use lines 101-102 from the Random Number Table to simulate 10 repetitions of randomly choosing 5 students and use your results to estimate the  HYPERLINK "JavaScript:top.Define('probability')" probability that all five students chosen got a B or better. How does this compare to the probability you calculated in part (c)? Explain. 2. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following  HYPERLINK "JavaScript:top.Define('distribution')" distribution (in millions of dollars):  INCLUDEPICTURE "http://ebooks.bfwpub.com/scc7e/tables/31_T_UN_3.gif" \* MERGEFORMATINET  What is the expected value of the profit? Interpret this value in a complete sentence in the context of the problem. Group 3 Probability Chapters 17-20 (continued) 1. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the  HYPERLINK "JavaScript:top.Define('distribution')" distribution of results:  INCLUDEPICTURE "http://ebooks.bfwpub.com/scc7e/tables/31_T_UN_6.gif" \* MERGEFORMATINET  Explain why this is a legitimate  HYPERLINK "JavaScript:top.Define('probabilitymodel')" probability model. What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that a randomly chosen student is studying a language other than English? (c) What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that a randomly chosen student is studying French, German, or Spanish? 2. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firms public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.) (a) Write down all possible choices of two of the five names. These are the possible outcomes. (b) The random drawing makes all outcomes equally likely. What is the  HYPERLINK "JavaScript:top.Define('probability')" probability of each outcome? (c) What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that Mei-Ling is chosen? (d) What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that neither of the two men (Sam and Roberto) is chosen? Group 4 Probability Chapters 17-20 (continued) 1. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to  HYPERLINK "JavaScript:top.Define('samplesurveys')" sample surveys that ask this question, 40% is about right.) A polling firm chooses an SRS of 1015 people. If they do this many times, the percentage of the  HYPERLINK "JavaScript:top.Define('sample')" sample who say they are very interested will vary from  HYPERLINK "JavaScript:top.Define('sample')" sample to  HYPERLINK "JavaScript:top.Define('sample')" sample following a  HYPERLINK "JavaScript:top.Define('normaldistribution')" Normal distribution withmean 40% and  HYPERLINK "JavaScript:top.Define('standarddeviation')" standard deviation 1.5%. Use the 689599.7 rule to answer these questions. (a) What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that one such  HYPERLINK "JavaScript:top.Define('sample')" sample gives a result within 1.5% of the truth about the population? (b) What is the  HYPERLINK "JavaScript:top.Define('probability')" probability that one such  HYPERLINK "JavaScript:top.Define('sample')" sample gives a result within 3% of the truth about the population? 2. There are 11 teams in the Big Ten athletic conference. Heres one set of  HYPERLINK "JavaScript:top.Define('personalprobability')" personal probabilities for next years basketball champion: Michigan State has  HYPERLINK "JavaScript:top.Define('probability')" probability 0.3 of winning. Iowa, Michigan, Illinois, Northwestern, and Penn State have no chance. That leaves 5 teams. Ohio State and Purdue both have the same  HYPERLINK "JavaScript:top.Define('probability')" probability of winning. Minnesota, Indiana, and Wisconsin also all have the same  HYPERLINK "JavaScript:top.Define('probability')" probability, but that  HYPERLINK "JavaScript:top.Define('probability')" probability is one-half that of Ohio State and Purdue. What  HYPERLINK "JavaScript:top.Define('probability')" probability does each of the 11 teams have? 3. Select from the word bank to fill in the blanks in the summary below. Words may be used more than once. sum randomness one probability very many zero and one proportion independent individual probabilities average curve adding area random digits  HYPERLINK "JavaScript:top.Define('randomness')" RANDOMNESS AND  HYPERLINK "JavaScript:top.Define('probability')" PROBABILITY __________________________________ describes the long-run regularity of random phenomena. The  HYPERLINK "JavaScript:top.Define('probability')" probability of an  HYPERLINK "JavaScript:top.Define('event')" event is the ___________________ of times the  HYPERLINK "JavaScript:top.Define('event')" event occurs in ____________________ repetitions of a random phenomenon. __________________________________________________ is unpredictable in the short run, and avoid seeking causal explanations for random occurrences.  HYPERLINK "JavaScript:top.Define('probabilitymodel')" PROBABILITY MODELS Any  HYPERLINK "JavaScript:top.Define('probability')" probability must be a number between ________________, and the total  HYPERLINK "JavaScript:top.Define('probability')" probability assigned to all possible outcomes must be _____________________. The  HYPERLINK "JavaScript:top.Define('probability')" probability that an  HYPERLINK "JavaScript:top.Define('event')" event does not occur is ________________ minus its __________________________. If two  HYPERLINK "JavaScript:top.Define('event')" events cannot occur at the same time, the  HYPERLINK "JavaScript:top.Define('probability')" probability that one or the other occurs is the ____________ of their _________________________________________. When  HYPERLINK "JavaScript:top.Define('probability')" probabilities are assigned to  HYPERLINK "JavaScript:top.Define('individual')" individual outcomes, find the  HYPERLINK "JavaScript:top.Define('probability')" _________________ of an  HYPERLINK "JavaScript:top.Define('event')" event by _________________________ the ___________________________________ of the outcomes that make it up. When  HYPERLINK "JavaScript:top.Define('probability')" probabilities are assigned by a Normal curve, find the  HYPERLINK "JavaScript:top.Define('probability')" probability of an  HYPERLINK "JavaScript:top.Define('event')" event by finding an ____________ under the __________________________. EXPECTED VALUE Expected value is the _________________________________________ of numerical outcomes in very many repetitions of a random phenomenon. D. SIMULATION Specify simple  HYPERLINK "JavaScript:top.Define('probabilitymodel')" probability models that assign  HYPERLINK "JavaScript:top.Define('probability')" probabilities to each of several stages when the stages are _______________________________ of each other. Assign  HYPERLINK "JavaScript:top.Define('randomdigits')" ______________________________________________ to simulate such models. Estimate either a  HYPERLINK "JavaScript:top.Define('probability')" probability or an expected value by repeating a simulation _____________________ times. Correct Answer (a) 68%. 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