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PRESENTATION OF STATISTICS

PRESENTATION OF STATISTICS. AQSAD RASHDA BS-4rth SEMESTER ZOOLOGY MAJOR ROLL # 16. TOPIC:. HYPOTHESIS TESTING ABOUT THE DIFFERENCE OF PROPORTIONS BETWEEN TWO POPULATIONS. Our data analysis journey continues. Proportion. Percent of a population that has some characteristic .

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PRESENTATION OF STATISTICS

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  1. PRESENTATION OF STATISTICS AQSAD RASHDA BS-4rth SEMESTER ZOOLOGY MAJOR ROLL # 16

  2. TOPIC: HYPOTHESIS TESTING ABOUT THE DIFFERENCE OF PROPORTIONS BETWEEN TWO POPULATIONS

  3. Our data analysis journey continues

  4. Proportion Percent of a population that has some characteristic. Proportion is of two forms: proportion of success and proportion of failure. Ref:1 Ref:1

  5. Why use proportion? • We focus on the most popular type of categorical response, the binary response. • Examples of binary responses • CURRENT_SMOKER: yes/no • SEX: male/female • SURVIVED: yes/no • DISEASE_STATUS.have disease or not.

  6. Test of difference of proportions for two populations: *Check whether samples drawn from same population or not. If two samples are drawn from different populations, we may be interested in finding out whether the difference between the proportion of successes is significant or not. Ref:2

  7. COMPARISON the comparison of two proportions p1 and p2 involves analyzing the difference between the two sample proportions, p^1 – p^2. Example: Number of people suffering from cholera in a village and in a city.

  8. PROPERTIES OF SAMPLING DISTRIBUTION OF p1-p2. • 1.p1-p2,unbiased estimator of π1-π2. • 2.standard error is standard deviation. • 3.Random samples. • 4. both sample sizes >30 .

  9. Procedure Hypothesis formulation Level of significance Test statistic calculations c.region conclusion

  10. Test statistic The test statistic z = (p1 -p2)/sp follows the standard normal distribution (with mean = 0 and standard deviation = 1).

  11. Conditions for comparison ~when the difference is zero. ~ when difference is not zero.

  12. Conditions

  13. Hypothesis Tests forTwo Population Proportions Population proportions Lower tail test: H0: p1 – p2 0 HA: p1 – p2< 0 Upper tail test: H0: p1 – p2≤ 0 HA: p1 – p2> 0 Two-tailed test: H0: p1 – p2= 0 HA: p1 – p2≠ 0 a a a/2 a/2 -za za -za/2 za/2 Reject H0 if z < -za Reject H0 if z > za Reject H0 if z < -za/2 or z > za/2 Ref:04

  14. 1.When difference is zero: ref:3

  15. When difference is zero:

  16. When difference is not zero: ref.4

  17. Example: Two population Proportions Is there a significant difference between the proportion of men and the proportion of women who will vote Yes on Proposition A? In a random sample, 36 of 72 men and 31 of 50 women indicated they would vote Yes Test at the .05 level of significance .

  18. The hypothesis test is: Example: Two population Proportions (continued) H0: p1 – p2= 0 (the two proportions are equal) HA: p1 – p2≠ 0 (there is a significant difference between proportions) • The sample proportions are: • Men: p1 = 36/72 = .50 • Women: p2 = 31/50 = .62 • The pooled estimate for the overall proportion is: aa

  19. Example: Two population Proportions (continued) Reject H0 Reject H0 The test statistic for p1 – p2 is: .025 .025 -1.96 1.96 -1.31 Decision:Do not reject H0 Conclusion:There is not significant evidence of a difference in proportions who will vote yes between men and women. Critical Values = ±1.96 For  = .05 a

  20. References: • 1.www.google.com. • 2.www.yahoo.com. • 3.”Statistics for utterly confused" by”Lioyd jaisingh”. • 4.”bussiness statistics" by" Ronald m weirs”. • 5.www.quickstar.com.

  21. **THE END** • aThanks a

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