invest_3ed.pdf

# A identify the observational units explanatory

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(a) Identify the observational units, explanatory variable, and response variable. Is this an observational study or an experiment? Observational units: Explanatory: Response: Type of study: Observational Experimental (b) Construct a two-way table to summarize the results of this study. Remember to put the explanatory variable in the columns. (c) Calculate the difference in the conditional proportions who survived (CC CPR). Does this seem to be a noteworthy difference to you? (d) Use technology to carry out Fisher’s Exact Test (by calculating the corresponding hypergeometric probability) to assess the strength of evidence that the probability of survival is higher with CC alone as compared to standard CPR. Write out how to calculate this probability, report the p-value, and interpret (on the next page) what it is the probability of. p-value = P(X ) = where X follows a hypergeometric distribution with N = , M = , and n =

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Chance/Rossman, 2015 ISCAM III Investigation 3.8 224 Interpretation: Because the sample sizes are large in this study, you should not be surprised that the distribution you examined in (d) is approximately normal. The large sample sizes allow us to approximate the hypergeometric distribution with a normal distribution. Thus, with large samples sizes (e.g., at least 5 successes and at least 5 failures in each group), an alternative to Fisher’s Exact Test is the two -sample z - test that you studied in Section 3.1. (e) Use technology to obtain the two-sample z -test statistic and p-value for this study. Compare this p- value to the one from Fisher’s Exact Test; are they similar? (f) Suggest a way of improving the approximation of the p-value. (g) (Optional): Compare the normal approximation not the hypergeometric calculation. [ Hints: In R, use iscamhypernorm(29, 518, 64, 278, TRUE) or use the Analyzing Two-way Tables applet to compare the normal approximation to the hypergeometric calculation.] (h) Do the data from this study provide convincing evidence that CC alone is better than standard CPR at the 10% significance level? Explain. How about the 5% level of significance? (i) An advantage to using the z -procedures is being able to easily produce a confidence interval for the parameter. Use technology to determine a 90 % confidence interval for the parameter of interest, and then interpret this interval. [ Hint : Think carefully about what the relevant parameter is in this study.]
Chance/Rossman, 2015 ISCAM III Investigation 3.8 225 (j) Suppose you had defined the parameter by subtracting in the other direction (e.g., CPR CC instead of CC CPR). How would that change: (i) the observed statistic? (ii) the test statistic? (iii) the p-value? (iv) confidence interval? Practice Problem 3.8 (a) Researchers in the CPR study also examined other response variables. For example, the 911 dispatcher’s instructions were completely delivered in 62% of episodes assigned to chest compression plus mouth-to-mouth compared to 81% of the episodes assigned to chest compression alone.

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