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# In summarizing your results remember to always

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In summarizing your results, remember to always conclude with an answer to the research question in context . The decision to reject or fail to reject H 0 should never be your last statement. Similarly, the determination of a confidence interval should never be the last statement. Include at least one more sentence interpreting the results in the context of the study, such as, the definition of the parameter estimated by this confidence interval, and how confident you are that the interval contains this parameter!

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Chance/Rossman, 2015 ISCAM III Investigation 1.5 52 Output from R The iscambinomtest includes some interesting graphs. The bottom graph illustrates the the 95% confidence interval. The interval is centered at the observed sample proportion p ˆ and then displays the two endpoints of the interval of plausible values for the process probability. The top graph shows the null distribution assuming the lower value of the confidence interval as the process probability. This is as far left as we can shift that distribution before the area to the right of p ˆ dips below 0.025. The middle graph shows how far we can move that distribution to the right (largest plausible value of ࠵? ) before the probability below p ˆ dips below 0.025. Practice Problem 1.5 (a) Recall the 8 out of 10 statistic for St. George’s Hospital (Investigation 1.3). Based on this result, what is an interval of plausible values for the underlying mortality rate at St. George’s ? [ Hint : You can use a 95% confidence level if none is stated.] To calculate the interval, first use the One Proportion Inference applet and trial-and-error, using multiples of 0.01 for potential parameter values. Then use technology to determine the 95% confidence interval more precisely. (b) Use technology to calculate the 95% confidence interval based on the 71 deaths among 361 patients. Comment on how the width and midpoint of this interval differ from the interval in (a). Explain why these changes make sense. (c) Based on the interval in (b), if you were to test H 0 : ࠵? = 0.20 vs. H a : ࠵? 0.20, would you reject or fail to reject the null hypothesis? Explain how you know.
Chance/Rossman, 2015 ISCAM III Investigation 1.5 53 Summary of Exact Binomial Inference (Sampling from a Binomial Process) Let X represent the number of successes in the sample and S the probability of success for the process. To test H 0 : S = S 0 We can calculate a p-value based on the binomial distribution with parameters n and S 0 . The p-value can be one-sided or two-sided based on the statement of the research conjecture. if H a : S > S 0 : p-value = P(X > observed ) if H a : S < S 0 : p-value = P(X < observed ) if H a : S S 0 : p-value = sum of both tail probabilities using a method like “small p - values” (100 × C )% Confidence Interval for S The set of values such that the two-sided p-value based on the observed count is larger than the (1 ± C ) cut-off.

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