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Cal Poly STAT 217 - Quantitative Data

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Winter, 2012 Monday, Feb. 6Stat 217 – Day 18Quantitative DataRecap: Can make statements about the difference in two population proportions- Reject H0: 1 – 2 = 0?o Obtain p-value from Two-way Table Simulation applet or Normal approximation (Testof Significance Calculator applet)o Test statistic measures the distance between the observed difference in sample proportions and the hypothesized difference in population proportions Z=Number of standard deviations above/below zero- Confidence interval for 1 – 2o Is zero a plausible value for the difference in population proportions?o Form: estimate + margin-of-errorExample: For the study comparing swimming with dolphins vs. just swimming, we could ask technology to calculate a confidence interval for the difference in the probability of substantial improvement.animal care control totalshowed substantial improvement 10 3 13did not show substantial improvement 5 12 17total 15 15 3095% CI for difference: (0.153799, 0.779534)(a) How would you interpret this interval?(b) But what’s wrong with this calculation?Example: A study reported in the Journal of the American Medical Association (1992) called into question the traditional value of 98.6o as the typical healthy body temperature. The researchers cite problems with Carl Wunderlich’s “axioms on clinical thermometry” and claim that the traditional value is out-of-date. Subjects were healthy men and women, aged 18-49 years, who were volunteers participating in Shigella vaccine trials at the University of MarylandCenter for Vaccine Development, Baltimore. The researchers took the subjects’ normal oral temperatures using a digital thermometer. Numerical and graphical summaries of the sample:Winter, 2012 Monday, Feb. 6 (a) Identify the observational units and the variable in this study. Classify the variable as quantitative or categorical.(b) How would you summarize the shape, center, and spread of this distribution?(c) Are the above values (98.249, .733) parameters or statistics? What symbols can we use to represent them?(d) Would you be surprised to randomly select a healthy adult and find their temperature to be 98.2oF?(e) What temperature(s) would someone have to have to be unusual?Winter, 2012 Monday, Feb. 6(f) Define, in words, the population parameter of interest. What symbol can we use to refer to this unknown value?(g) Suppose we want to carry out a test of significance for these data, state the null and alternative hypotheses (in symbols) for testing whether the average body temperature of the population of healthy adults appears to be 98.6 or not. (h) Suppose the null hypothesis is true, would you be surprised to find an average of 130 healthy adults to be 98.249oF? What additional information do you need to have?(i) Is it more surprising or less surprising than finding one person to have a temperature of 98.249oF when the population mean equals 98.6?(j) What about a sample of 1300 healthy adults?Winter, 2012 Monday, Feb. 6Example: Below is a dotplot of the weights of the 2008 Men’s Olympic Rowing Team (in lbs).Name Event Weight Name Event WeightAllen Eight 216 Newlin Four 229Altman LW Four 161 Paradiso LW Four 154Banks Double Sculls 194 Piermarini Double Sculls 205Boyd Eight 209 Schnobrich Eight 205Coppola Eight 220 Schroeder Quad Sculls 225Daly LW Four 161 Stitt Quad Sculls 200Gault Quad Sculls 209 Teti Four 181Hoopman Eight 200 Todd LW Four 159Hovey Pair 205 Volpenhein Four 225Hughes Quad Sculls 205 Walsh Eight 220Inman Eight 209 Winklevoss, C. Quad Sculls 209Lanzone Four 218 Winklevoss, T. Pair 209Mc Elhenney Eight 121 (a) Describe the shape, center, and spread of this distribution based on the dotplot. (b) Why do you think there is a separate cluster around 160lbs?(c) Why do you think there is one weight that is much smaller than the rest? (d) If that lightest rower was removed from the data set, how would the mean and SD


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