Lecture on Two-Sample Hypothesis Testing

1. Two-Sample Hypothesis Testing Allows for direct comparisons between two groups…

2. TWO-SAMPLE HYPOTHESIS TESTING For the population mean, either ni < 30

5. The sampling distribution of the difference between means is also normally distributed… …if both sample sizes are above 30 If this is not the case, must use the t-distribution to perform the hypothesis test… The t-distribution is described by degrees of freedom (which depends on the sample size) For a two-sample test, df = (n1-1) + (n2-1) = n1 + n2 -2

6. The sampling distribution of the difference between means follows the t-distribution …if at least one sample sizeis below 30 OBSERVED VALUES tOBSstandardize the difference between sample means (calculate a z-score [t-score])

7. OBSERVED VALUES tOBS Since variability is critical to this distribution, we need to ensure that the variance of the two groups can be considered ‘equal’… …if so, we pool the two sample variances to get one estimate

8. OBSERVED VALUES tOBS =STANDARDIZE P-value =TDIST(|tOBS|, df, # of tails) NULL: μ1 - μ2 ≥ 0 0

9. CRITICAL VALUES t-distribution Region of Rejection Region of Rejection Critical Values tCRIT=TINV(2a/# of tails, df) a= 0.05

11. p-value < α-level?…then REJECT the NULL

13. p-value < α-level?…then REJECT the NULL

14. TWO-SAMPLE HYPOTHESIS TESTING For the population proportion

17. The sampling distribution of the difference between proportions follows the normal distribution OBSERVED VALUES zOBSstandardize the difference between sample proportions (calculate a z-score ) where p is the common proportion…

19. p-value < α-level?0 zOBS= STANDARDIZE((p1-p2), (p1- p 2), ) zCRIT= NORMSINV(1-/# of tails) p-value =(# of tails) * (1-NORMSDIST(|zOBS|)) …then REJECT the NULL