In this study we found that the amount of time a

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In this study, we found that the amount of time a blocked driver waits before responding follows a skewed right distribution with a mean of 4.25 seconds and a median of 3.24 seconds, with a few drivers waiting more than 10 seconds. Although the dataset is small, we might consider using these data to build a mathematical model (for these skewed data either using a transformation or a probability model other than the normal distribution) to help predict future results (e.g., a wait time of less than 2 seconds). These researchers were actually interested in whether the “social status” of the blocked car was related to how long it took before people honked. They found that “the mean and median response times decreased monotonically with the statu s of car, except when the blocked car was very small.” Similar results had been found in an earlier study by Doob and Gross in the United States (1968) which varied the status of the blocking car. However, neither study was replicated by a Swiss study (Jann, Suhner, & Marioni, 1995), perhaps due to cultural differences impacting generalizability. Practice Problem 2.2A A group of Cal Poly students (Sasscer, Mease, Tanenbaum, and Hansen, 2009) conducted the following study: volunteers were to say “go,” and then to say “stop” when they believed 30 seconds had passed. The researches asked the participants to not count in their heads and recorded how much time had actually passed. The data are in 30seconds.txt . (a) Examine graphical and numerical summaries of these data. Describe the shape of the distribution. How do the mean and median compare? What does this tell you about whether people tend to over or underestimate the length of 30 seconds? (b) Does a normal model seem appropriate here? (c) Does a log transformation succeed in creating a normal distribution? Explain how you might have predicted this answer based on the first graph you looked at. (d) To what population would you be willing to generalize these data? Practice Problem 2.2B Below are distribution fits for the honking data with a Weibull distribution and a Gamma distribution. Weibull Gamma Which do you think indicates a better fit for these data? Explain how you are deciding.
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Chance/Rossman, 2015 ISCAM III Investigation 2.3 148 Investigation 2.3: Readability of Cancer Pamphlets Researchers in Philadelphia investigated whether or not pamphlets containing information for cancer patients are written at a level that the cancer patients can comprehend. They applied tests to measure the reading levels of 63 cancer patients and also the readability levels of 30 cancer pamphlets (based on such factors as sentence length and number of polysyllabic words). These numbers correspond to grade levels, but cancer patient reading levels below grade 3 and above grade 12 were not determined exactly.
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