Comparing Two Proportions

1. Comparing Two Proportions Part 2, the practice

2. When we want to compare to proportions (groups) we need to combine the variances of each group. We always add variances, never subtract even if we want to compare differences because when we combine or take the difference, the variations of each sample come together to give us more variation rather than less. 2 are less likely to agree than one is by themselves. Pg 1.2 when do you pool?

3. Difference between 2 proportions: What are the steps to creating a 2-prop confidence interval? • = Z* = SE = ME = • Interval: • Conclusion: Pg 1.3 how do you find the SE? Pg 1.4 what does the interval mean?

4. Difference between 2 proportions: What are the steps to doing a 2-prop hypothesis test? State your conclusion: Pg 1.5 why pool samples? Pg 1.6 what does the p-value mean?

5. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones?

6. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? a) What kind of design was used to collect these data? Pg 2.2

7. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? b) Are the assumptions and conditions necessary for inference satisfied? Pg 2.3

8. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? c) Construct a 95% confidence interval. Pg 2.4

9. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? d) Explain in context the confidence interval.

10. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? e) Write appropriate hypothesis statements • Ho: Ha: p(pooled): q(pooled): Pg 2.5

11. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? f) Test the hypothesis and state your conclusion. • SE(pooled) : z-score: p-value: • Conclusion: Pg 2.6

12. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? g) Explain in this context what your P-value means.

13. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression , and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than non-depressed ones? h) If your conclusion is actually incorrect, which type of error did you commit? Pg 2.7

14. Great Britain has a great literary tradition that spans centuries. One might assume, then, that Britons read more than citizens of other countries. Some Canadians, however, feel that a higher percentage of Canadians than Britons read. A recent Gallup Poll reported that 86% of 1004 randomly sampled Canadians read at least one book in the past year, compared to 81% of 1009 randomly sampled Britons. Do these results confirm a higher reading rate in Canada? Find a 99% confidence interval for the difference in the proportion of Britons and Canadians who read at least one book in the last year. Interpret your interval.

15. Great Britain has a great literary tradition that spans centuries. One might assume, then, that Britons read more than citizens of other countries. Some Canadians, however, feel that a higher percentage of Canadians than Britons read. A recent Gallup Poll reported that 86% of 1004 randomly sampled Canadians read at least one book in the past year, compared to 81% of 1009 randomly sampled Britons. Do these results confirm a higher reading rate in Canada? • = Z* = SE = ME = • Interval: • Conclusion: Assumptions:

16. Great Britain has a great literary tradition that spans centuries. One might assume, then, that Britons read more than citizens of other countries. Some Canadians, however, feel that a higher percentage of Canadians than Britons read. A recent Gallup Poll reported that 86% of 1004 randomly sampled Canadians read at least one book in the past year, compared to 81% of 1009 randomly sampled Britons. Do these results confirm a higher reading rate in Canada? Test an appropriate hypothesis and state your conclusions.

17. Great Britain has a great literary tradition that spans centuries. One might assume, then, that Britons read more than citizens of other countries. Some Canadians, however, feel that a higher percentage of Canadians than Britons read. A recent Gallup Poll reported that 86% of 1004 randomly sampled Canadians read at least one book in the past year, compared to 81% of 1009 randomly sampled Britons. Do these results confirm a higher reading rate in Canada? Assumptions: • Ho: Ha:  = • z-score = p-value = • Conclusion:

18. End