invest_3ed.pdf

# Practice problem 411 another aspect of this same

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Practice Problem 4.11 Another aspect of this same study considered not just whether the child woke up but whether he/she successfully escaped from the house within 5 minutes of the alarm sounding. The article reports that 20 children escaped when they heard the mother’s voice, and only 9 escaped when they heard the conventional tone. (a) Describe what additional information you need before you can analyze the data as you did above. (b) Two children did not escape to either kind of alarm. Use this information to complete the following table: Escaped to conventional alarm Did not escape to conventional alarm Total Escaped to mother’s voice 20 Did not escape to mother’s voice Total 9 24 (c) Conduct a simulation analysis (with the One Proportion Inference applet) of these data. Be sure to describe how you use the applet, and report an approximate p-value. (d) Use the binomial distribution to calculate the exact p-value for this test. (e) Summarize your conclusion from this “escaping within 5 minutes” aspect of the study, and explain the reasoning process behind your conclusion.

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Chance/Rossman, 2015 ISCAM III Example 4.1 306 Example 4.1: Age Discrimination? Try these questions yourself before you use the solutions following to check your answers. In Investigation 4.1, you considered the case of Robert Martin and whether the sample of 10 employees in his department provided evidence of age discrimination. Suppose we decide to focus on the long-run difference in mean ages for those laid-off and those retained for the decision making process used by this company. (a) State the null and alternative hypotheses, in symbols, for this study. [ Hint : Define your symbols.] (b) Recall the observed value of the sample statistic. (c) Simulate a randomization test for these data and state your conclusion at the 0.01 level of significance. (d) Carry out a two-sample t -test for these data and hypotheses, and state your conclusion at the 0.01 level of significance. (e) Do these analyses reach the same conclusion? If not, which analysis should be used? Explain. Analysis (a) Let P fired ± P not fired represent the difference in the average age of people that would be laid-off, in the long run (by the overall process), and the average age of the people who would be retained. ( Don’t worry too much at this point about which stage of the firing process this analysis considers. Just keep in mind that we are trying to say something beyond the observed means. We believe there is some underlying difference in means and these data provide an estimate.) H 0 : P fired ± P not fired = 0 (no overall difference in the average ages of those getting fired and not) H a : P fired ± P not fired > 0 (those getting fired will tend to have higher ages than those not) (b) 2 1 x x ± = 58.00 41.14 = 16.86 years
Chance/Rossman, 2015 ISCAM III Example 4.1 307 (c) Using the Comparing Groups (Quantitative) applet, the empirical p-value (remembering to match the direction of subtraction, which may vary depending on how you pasted the data in), the output below shows an empirical p-value of 0.0225. Because 0.0225 > 0.01, we would not reject the null hypothesis at

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