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Topic 21—Comparison of Proportions

Topic 21—Comparison of Proportions. Example. Test of Significance – Problem #1. A test of significance for the difference of two proportions Requirements: Indep . SRS or Random assign. t o groups? Randomly assigned to groups—OK . Results should be valid.

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Topic 21—Comparison of Proportions

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  1. Topic 21—Comparison of Proportions Example

  2. Test of Significance – Problem #1 • A test of significance for the difference of two proportions • Requirements: • Indep. SRS or Random assign. to groups? • Randomly assigned to groups—OK • . • Results should be valid

  3. Ho: Pa = Pp The proportion of all HIV+ people who develop AIDS on AZT equals proportion of HIV+ people who develop AIDS on placebo • Ha: Pa < Pp The proportion of all HIV+ people who develop AIDS on AZT is less than the proportion of HIV+ people who develop AIDS on placebo • Z = • P(z<-2.9256) = .0017

  4. Because our p-value is less than 5%, we reject the null hypothesis. We have enough evidence to conclude that the proportion of HIV+ people who develop AIDS on AZT is less than the proportion of HIV+ people who develop AIDS on a placebo.

  5. Confidence Interval – Problem #1 • 95% confidence interval to estimate the difference between 2 proportions • Requirements • Same as above • . • .

  6. (-.0805, -.0161) • I am 95% confident that the true difference between the proportions who developed AIDS between the AZT and placebo groups is between -.0805 and -.0161 • ***AZT group developed AIDS between 1.6% and 8% less often.

  7. Test of Significance – Problem #2 • A test of significance for the difference of two proportions • Requirements: • Indep. SRS or Random assign. to groups? • Indep groups (urban vs. rural) but unsure how chosen-X • . • Results may be questionable

  8. Ho: Purb= PrurThe proportion of urban students who pass course in chemical engineering at NC St. equals the proportion of rural students who pass the same course. • Ha: Purb≠PrurThe proportion of urban students who pass course in chemical engineering at NC St. does not equal the proportion of rural students who pass the same course. • Z = • 2 x P(z>|2.987|) = .0028

  9. Because our p-value is less than 5%, we reject the null hypothesis. We have enough evidence to conclude the proportion of urban students who pass course in chemical engineering at NC St. does not equal the proportion of rural students who pass the same course .

  10. Confidence Interval – Problem #2 • 90% confidence interval to estimate the difference between 2 proportions • Requirements • Same as above • . • .

  11. (.11723, .39186) • I am 90% confident that the true difference between the proportions of urban students who pass the chemical engineering class at NC St. and the proportion of rural students who pass the class is between .11723 and .39186.

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