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Comparing Two Proportions

Comparing Two Proportions. chapter 22 -Assumptions and conditions for comparing two proportions -Finding a confidence interval -Test an appropriate hypthoesis.

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Comparing Two Proportions

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  1. Comparing Two Proportions chapter 22 -Assumptions and conditions for comparing two proportions -Finding a confidence interval -Test an appropriate hypthoesis

  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.

  3. A recent survey of 886 randomly selected teenagers (12-17) found that more than half of them had online profiles. Some researchers are concerned about the possible access to personal information about teens in public places on the internet. There appear to be differences between boys and girls in their online behavior. Among teens ages 15 to 17, 57% of the 248 boys had posted profiles compared to 70% of the 256 girls. Is there a difference between boys and girls behavior? Is this difference normal variation in the samples or is there really a difference between the groups? Independence : (unit and group) Randomization: 10% : Success/Failure: • (sample size big enough)

  4. A recent survey of randomly selected teenagers (12-17) found that more than half of them had online profiles. Among teens, 57% of the 248 boys had posted profiles compared to 70% of the 256 girls. Is there a difference between boys and girls behavior? Create a 95% confidence interval for the difference in online behavior. • = Z* = SE = ME = • Interval: • Conclusion:

  5. A recent survey of randomly selected teenagers (12-17) found that more than half of them had online profiles. Among teens, 57% of the 248 boys had posted profiles compared to 70% of the 256 girls. Is there a difference between boys and girls behavior? Test an appropriate hypothesis of online behavior for the difference between males and females. • To get a more accurate SE we pool the data! We only do this with hypothesis tests NOT confidence Intervals. Click for Formulas

  6. A recent survey of randomly selected teenagers (12-17) found that more than half of them had online profiles. Among teens, 57% of the 248 boys had posted profiles compared to 70% of the 256 girls. Is there a difference between boys and girls behavior? Test an appropriate hypothesis of online behavior for the difference between males and females. • Ho: Ha: p(pooled): q(pooled): • SE(pooled) : z-score: p-value: • Conclusion: Click for Formulas

  7. A recent survey of randomly selected teenagers (12-17) found that more than half of them had online profiles. Among teens, 57% of the 248 boys had posted profiles compared to 70% of the 256 girls. Is there a difference between boys and girls behavior? Test an appropriate hypothesis of online behavior for the difference between males and females. • Ho: Ha: p(pooled): q(pooled): • SE(pooled) : z-score: p-value: • Conclusion:

  8. Class Example C: A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? Is this difference normal variation in the samples or is there really a difference between the groups?

  9. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? Confidence Interval(never pool) confidence level: SE:  ME: Interval:

  10. A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. 177 men and 159 women respond that they have a positive impression of the candidate. Is there a gender gap? Hypothesis Test (pool the data for better SE) • Ho: Ha: p(pooled): q(pooled): • SE(pooled) : z-score: p-value: • Conclusion:

  11. Comparing Two Proportions Use the Lesson check on the web page to record your answers to the following questions.

  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?

  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? a) What kind of design was used to collect these data?

  14. 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?

  15. 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.

  16. 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.

  17. 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):

  18. 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:

  19. 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.

  20. 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?

  21. End

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