K based on this analysis what conclusions would you

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(k) Based on this analysis, what conclusions would you draw about the probability of death within 30 days of a heart transplant at this hospital? Does it matter which outcome I choose to be success? (l) Suppose that we had focused on survival for 30 days rather than death within 30 days as a “success” in this study. Describe how the hypotheses would change and how the calculation of the binomial p- value would change. Then go ahead and calculate the exact binomial p-value with this set-up. How does its value compare to your answer in (j)? How (if at all) does your conclusion change? Does the sample size matter? (m) Following up on the suspicion that the sample of size 10 aroused, these researchers proceeded to gather data on the previous 361 patients who received a heart transplant at this hospital dating back to 1986. They found 71 deaths. Calculate the sample proportion for these data: Predict whether this i s more or less convincing evidence that this hospital’s death rate exceeds 0.15? Explain your reasoning. Use the One Proportion Inference applet to determine (approximately with simulation, and exactly with the binomial distribution) the probability of finding at least 71 deaths in a sample of 361 if S = 0.15.
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Chance/Rossman, 2015 ISCAM III Investigation 1.3 43 (n) Is the probability in (m) convincing evidence to consider the sample result surprising if the mortality rate at this hospital matched the national rate? Explain. (o) Is the evidence against the null hypothesis stronger or weaker than the earlier analysis based on 10 deaths? Explain how you are deciding and why the strength of evidence has changed in this manner. The following graphs display the two theoretical probability distributions (for sample sizes n = 10 and n = 361), both assuming the null hypothesis ( S = 0.15) is true. These graphs show just how far the observed values (8 and 71) are from the expected value of the number of deaths (0.15 × 10 = 1.5 and 0.15 × 361 = 54.15) in each case. You should also note that the shape, center, and variability of the probability distribution for number of successes are all affected by the sample size n . Keep in mind that of interest to us is our observation’s relative location in the null distribution. Thus, we are most interested in how variable the possible outcomes are from the “expected” outcome. The center of the distribution isn’t all that interesting to us in answering the research question because we determine what the center of the distribution will be by how we specify the null model. Even the shape isn’t all that interesting for its own sake in answering our research question. (p) Identify one other feature of the above distributions that differs between them.
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Chance/Rossman, 2015 ISCAM III Investigation 1.3 44 (q) Which data set do you think is more valid to use the larger sample size or the more recent data?
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