invest_3ed.pdf

E translate your answers to c and d to a null and

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(e) Translate your answers to (c) and (d) to a null and alternative hypothesis statements. Keep in mind, the null hypothesis claims the observed result is “just by chance,” whereas the alternative hypothesis translates the research conjecture. Null hypothesis (often denoted H 0 ): Alternative hypothesis (often denoted H a ):

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Chance/Rossman, 2015 ISCAM III Investigation 1.3 41 (f ) Of the hospital’s ten most recent transplantations at the time of the study, there had been eight deaths within the first 30 days following surgery. Is this sample result in the direction suspected by the researchers? Explain. What symbol could we use to refer to this proportion? (g) Describe two methods for obtaining a p-value to assess whether this observed result is statistically signi ficant. (Be sure it’s clear what is different in this scenario from what you did in previous investigations.) Recap: We have seen two main ways to obtain a p-value to assess the strength of evidence these data provide against the claim that the mortality rate at this hospital could be 0 .15. What’s differe nt now is that we are interested in testing a null probability other than 0.5. Approach 1: Simulation Assume the mortality rate is 0.15 and generate thousands of samples of 10 patients, counting the number that die in each sample. Examine this null distribution to see how unusual it is to find 8 or more patients dying in the sample by chance alone. (Previously, we looked at both physical coin tossing and the One Proportion Inference applet as ways to simulate these outcomes with a success probability of S = 0.5. Now we can’t use coins but we could use spinners for a physical model of this random process.) Approach 2: Exact binomial probabilities Use binomial probabilities to calculate the long-run relative frequency of 8 or more deaths from a binomial process with n = 10 and S = 0.15. That is, determine P(X > 8) where X represents the number of successes. You could calculate this probability by hand using the formula or with technology (R (either iscambinomprob or iscambinomtest ), or Minitab, or the One Proportion applet). With either approach, a small p-value provides evidence against the null hypothesis underlying the calculation (we “reject the null hypothesis” as being p lausible based on what we observed). If you examine enough samples in the simulation, your result will be quite close to the exact binomial approach. (h) Open the One Proportion Inference applet and generate 1000 samples from a binomial process with S = 0.15 (under the null model) and n = 10. Comment on the shape of the distribution. (i) Estimate the p-value from this null distribution. Clearly explain how you did so.
Chance/Rossman, 2015 ISCAM III Investigation 1.3 42 (j) Check the Exact Binomial box to have the applet determine the exact p-value. Report and interpret this value below (what is it the probability of?).

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