lecture8 - ECO201 Lecture8 HypothesisTesting: ZandtTests...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
ECO 201 Lecture 8 Hypothesis Testing:   and  t   Tests
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Topics Tests for the Difference between Two  Proportions Testing for the Difference Between the Means  of Two Independent Groups Paired  t   Test
Background image of page 2
Two-Sample Tests Two-Sample Tests Population Means, Independent Samples Means, Related Samples Population 1 vs. independent Population 2 Same population before vs. after treatment Examples: Population Proportions Proportion 1 vs. Proportion 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Hypothesis Tests for Two Population Proportions Goal: test a hypothesis or form a confidence interval for the difference between two population proportions, π 1 π 2 The _____________ for the difference is Population proportions Assumptions: n 1 π 1 5 , n 1 (1- π 1 ) 5 n 2 π 2 5 , n 2 (1- π 2 ) 5 2 1 p p -
Background image of page 4
Confidence Interval for Two Population Proportions Population proportions ( 29 2 2 2 1 1 1 2 1 n ) p (1 p n ) p (1 p Z p p - + - ± - The confidence interval for π 1 π 2 is:
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Hypothesis Tests for Two Population Proportions Population proportions tail test: H 0 : π 1 π 2 H 1 : π 1 < π 2 i.e., H 0 : π 1 π 2 0 H 1 : π 1 π 2 < 0 tail test: H 0 : π 1 π 2 H 1 : π 1 > π 2 i.e., H 0 : π 1 π 2 ≤ 0 H 1 : π 1 π 2 > 0 Two-tail test: H 0 : π 1 = π 2 H 1 : π 1 π 2 i.e., H 0 : π 1 π 2 = 0 H 1 : π 1 π 2 ≠ 0
Background image of page 6
Hypothesis Tests for Two Population Proportions Population proportions Lower-tail test: H 0 : π 1 π 2 0 H 1 : π 1 π 2 < 0 Upper-tail test: H 0 : π 1 π 2 ≤ 0 H 1 : π 1 π 2 > 0 Two-tail test: H 0 : π 1 π 2 = 0 H 1 : π 1 π 2 ≠ 0 α α /2 α /2 α -z α -z α /2 z α z α /2 Reject H 0 if Z < -Z α Reject H 0 if Z > Z α Reject H 0 if Z < -Z α/2 or Z > Z α/2 (continued)
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example:  Z Test for Difference in 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
Background image of page 8
The hypothesis test is: H 0 : π 1 π 2 = (the two proportions are equal) H 1 : π 1 π 2 (there is a significant difference between proportions) The sample proportions are: Men:   p 1  = 36/72 = .50 Women:   p 2  = 31/50 = .62 .549 122 67 50 72 31 36 n n X X p 2 1 2 1 = = + + = + + = The pooled estimate for the overall proportion is: Example:  Z Test for Difference in Two population  Proportions (continued)
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Z Test for the Difference Between  Two Proportions Add-Ins (tab)|Menu Commands|PHStat  |  Two-Sample Tests  |  Z Test for Differences  in Two Proportions …   Double Click Here  for Excel Output
Background image of page 10
Excel output: Z Test for Differences in Two Proportions Hypothesized Difference 0 Level of Significance 0.05 Group 1 Number of Successes 36 Sample Size 72 Group 2 Number of Successes 31 Sample Size 50 Group 1 Proportion 0.5 Group 2 Proportion 0.62 Difference in Two Proportions -0.12 Average Proportion 0.549180328 Z Test Statistic -1.310067478
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 40

lecture8 - ECO201 Lecture8 HypothesisTesting: ZandtTests...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online