Aspirin III: Decision and Conclusion 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 Which of the following options are correct? (Two are correct: one for the decision, and one for the conclusion. Find and select both of them.) Group of answer choices ( ) This data provides strong evidence that aspirin has NO effect on one's risk of developing cancer. ( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we reject the Null Hypothesis. ( ) 7.214% of the aspirin users developed cancer, whereas only 7.156% of the members of the placebo group developed cancer. Hence we can conclude that using aspirin slightly increases one's risk of developing lung cancer. ( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we fail to reject the Null Hypothesis. ( ) This data provided very little evidence that using aspirin has any effect on one's risk of developing cancer. ( ) This data provided strong evidence that aspirin affects one's risk of developing cancer.

Aspirin III: Decision and Conclusion 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 Which of the following options are correct? (Two are correct: one for the decision, and one for the conclusion. Find and select both of them.) Group of answer choices ( ) This data provides strong evidence that aspirin has NO effect on one's risk of developing cancer. ( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we reject the Null Hypothesis. ( ) 7.214% of the aspirin users developed cancer, whereas only 7.156% of the members of the placebo group developed cancer. Hence we can conclude that using aspirin slightly increases one's risk of developing lung cancer. ( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we fail to reject the Null Hypothesis. ( ) This data provided very little evidence that using aspirin has any effect on one's risk of developing cancer. ( ) This data provided strong evidence that aspirin affects one's risk of developing cancer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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Aspirin III: Decision and Conclusion

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

Which of the following options are correct? (Two are correct: one for the decision, and one for the conclusion. Find and select both of them.)

Group of answer choices

( ) This data provides strong evidence that aspirin has NO effect on one's risk of developing cancer.

( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we reject the Null Hypothesis.

( ) 7.214% of the aspirin users developed cancer, whereas only 7.156% of the members of the placebo group developed cancer. Hence we can conclude that using aspirin slightly increases one's risk of developing lung cancer.

( ) Since the P-value is 0.8224, which is bigger than our usual cut-off of 0.05, we fail to reject the Null Hypothesis.

( ) This data provided very little evidence that using aspirin has any effect on one's risk of developing cancer.

( ) This data provided strong evidence that aspirin affects one's risk of developing cancer.

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