1 / 32

Two Sample Tests

Two Sample Tests. TEST FOR EQUAL VARIANCES. TEST FOR EQUAL MEANS. H o. H o. Population 1. Population 1. Population 2. Population 2. H a. H a. Population 1. Population 2. Population 1. Population 2. Hypothesis Tests for Two Population Variances. Two-Tailed Test.

walker
Download Presentation

Two Sample Tests

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Two Sample Tests TEST FOR EQUAL VARIANCES TEST FOR EQUAL MEANS Ho Ho Population 1 Population 1 Population 2 Population 2 Ha Ha Population 1 Population 2 Population 1 Population 2

  2. Hypothesis Tests for Two Population Variances Two-Tailed Test Upper One-Tailed Test Lower One-Tailed Test

  3. Hypothesis Tests for Two Population Variances F-TEST STATISTIC FOR TESTING WHETHER TWO POPULATIONS HAVE EQUAL VARIANCES where: ni = Sample size from ith population nj = Sample size from jth population si2= Sample variance from ith population sj2= Sample variance from jth population

  4. Hypothesis Tests for Two Population Variances(Example 9-2) df: Di = 10, Dj =12 a = .10 Rejection Region /2 = 0.05 F = 1.47 F 0 Since F=1.47  F/2= 2.76, do not reject H0

  5. Independent Samples Independent samples Selected from two or more populations Values in one sample have no influence on the values in the other sample(s).

  6. Hypothesis Tests for Two Population Means Two-Tailed Test Upper One-Tailed Test Lower One-Tailed Test Format 1

  7. Hypothesis Tests for Two Population Means Two-Tailed Test Upper One-Tailed Test Lower One-Tailed Test Format 2

  8. Hypothesis Tests for Two Population Means T-TEST STATISTIC (EQUAL POPULATION VARIANCES) where: Sample means from populations 1 and 2 Hypothesized difference Sample sizes from the two populations Pooled standard deviation

  9. Hypothesis Tests for Two Population Means POOLED STANDARD DEVIATION Where: s12 = Sample variance from population 1 s22 = Sample variance from population 2 n1 and n2 = Sample sizes from populations 1 and 2 respectively

  10. Hypothesis Tests for Two Population Means (Unequal Variances) t-TEST STATISTIC where: s12 = Sample variance from population 1 s22 = Sample variance from population 2

  11. Hypothesis Tests for Two Population Means (Example 9-4) Rejection Region  /2 = 0.025 Rejection Region  /2 = 0.025 Since t < 2.048, do not reject H0

  12. Hypothesis Tests for Two Population Means DEGREES OF FREEDOM FOR t-TEST STATISTIC WITH UNEQUAL POPULATION VARIANCES

  13. Confidence Interval Estimates for 1 - 2 STANDARD DEVIATIONS UNKNOWN AND12 = 22 where: = Pooled standard deviation t/2 = critical value from t-distribution for desired confidence level and degrees of freedom equal to n1 + n2 -2

  14. Confidence Interval Estimates for 1 - 2(Example 9-5) - $330.46 $1,458.34

  15. Confidence Interval Estimates for 1 - 2 STANDARD DEVIATIONS UNKNOWN AND12  22 where: t/2 = critical value from t-distribution for desired confidence level and degrees of freedom equal to:

  16. Confidence Interval Estimates for 1 - 2 LARGE SAMPLE SIZES where: z/2 = critical value from the standard normal distribution for desired confidence level

  17. Paired Samples Hypothesis Testing and Estimation Paired samples are samples that selected such that each data value from one sample is related (or matched) with a corresponding data value from the second sample. The sample values from one population have the potential to influence the probability that values will be selected from the second population.

  18. Paired Samples Hypothesis Testing and Estimation PAIRED DIFFERENCE where: d = Paired difference x1 and x2 = Values from sample 1 and 2, respectively

  19. Paired Samples Hypothesis Testing and Estimation MEAN PAIRED DIFFERENCE where: di = ith paired difference n = Number of paired differences

  20. Paired Samples Hypothesis Testing and Estimation STANDARD DEVIATION FOR PAIRED DIFFERENCES where: di = ith paired difference = Mean paired difference

  21. Paired Samples Hypothesis Testing and Estimation t-TEST STATISTIC FOR PAIRED DIFFERENCES where: = Mean paired difference d = Hypothesized paired difference sd = Sample standard deviation of paired differences n = Number of paired differences

  22. Paired Samples Hypothesis Testing and Estimation(Example 9-6) Rejection Region  = 0.05 Since t=0.9165 < 1.833, do not reject H0

  23. Paired Samples Hypothesis Testing and Estimation PAIRED CONFIDENCE INTERVAL ESTIMATE

  24. Paired Samples Hypothesis Testing and Estimation(Example 9-7) 95% Confidence Interval 4.927 9.273

  25. Hypothesis Tests for Two Population Proportions Two-Tailed Test Upper One-Tailed Test Lower One-Tailed Test Format 1

  26. Hypothesis Tests for Two Population Proportions Two-Tailed Test Upper One-Tailed Test Lower One-Tailed Test Format 2

  27. Hypothesis Tests for Two Population Proportions POOLED ESTIMATOR FOR OVERALL PROPORTION where: x1 and x2 = number from samples 1 and 2 with desired characteristic.

  28. Hypothesis Tests for Two Population Proportions TEST STATISTIC FOR DIFFERENCE IN POPULATION PROPORTIONS where: (1 - 2) = Hypothesized difference in proportions from populations 1 and 2, respectively p1 and p2 = Sample proportions for samples selected from population 1 and 2 = Pooled estimator for the overall proportion for both populations combined

  29. Hypothesis Tests for Two Population Proportions (Example 9-8) Rejection Region  = 0.05 Since z =-2.04 < -1.645, reject H0

  30. Confidence Intervals for Two Population Proportions CONFIDENCE INTERVAL ESTIMATE FOR 1- 2 where: p1 = Sample proportion from population 1 p2 = Sample proportion from population 2 z = Critical value from the standard normal table

  31. Confidence Intervals for Two Population Proportions(Example 9-10) -0.034 0.104

  32. Independent Samples Paired Samples Key Terms

More Related