Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows: p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did. p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did. They ran the code for a two-sided significance test and got the following results: ## ## ## Inferential Procedures for the Difference of Two Proportions p1-p2: ## cancer grouped by treatment ## ## ## Descriptive Results: ## ## yes n estimated.prop ## Aspirin 1438 19934 0.07214 ## Placebo 1427 19942 0.07156 ## ## ## Inferential Results: ## ## Estimate of p1-p2: 0.0005805 ## SE(p1.hat - p2.hat): 0.002586 ## ## 95% Confidence Interval for p1-p2: ## ## lower.bound upper.bound ## -0.004489 0.005650 ## ## Test of Significance: ## ## H_0: p1-p2 = 0 ## H_a: p1-p2 != 0 ## ## Test Statistic: z = 0.2245 ## P-value: P = 0.8224 Regarding the "safety" of applying porptestGC() to the situation, which of the following remarks are good to make? (There are two correct answers.)
Aspirin II: Safety Considerations
Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows:
p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did.
p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did.
They ran the code for a two-sided significance test and got the following results:
##
##
## Inferential Procedures for the Difference of Two Proportions p1-p2:
## cancer grouped by treatment
##
##
## Descriptive Results:
##
## yes n estimated.prop
## Aspirin 1438 19934 0.07214
## Placebo 1427 19942 0.07156
##
##
## Inferential Results:
##
## Estimate of p1-p2: 0.0005805
## SE(p1.hat - p2.hat): 0.002586
##
## 95% Confidence Interval for p1-p2:
##
## lower.bound upper.bound
## -0.004489 0.005650
##
## Test of Significance:
##
## H_0: p1-p2 = 0
## H_a: p1-p2 != 0
##
## Test Statistic: z = 0.2245
## P-value: P = 0.8224
Regarding the "safety" of applying porptestGC() to the situation, which of the following remarks are good to make? (There are two correct answers.)
( ) In order to make confidence intervals and P-values, proptestGC() uses the normal-curve approximation. This approximation may not be good unless there are at least ten successes and at least ten failures in each sample. This time we have thousands of successes and thousands of failures in each sample. We also did a randomized experiment, so in all relevant respects it is safe to use proptestGC().
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