STAT 213 Lecture Notes - Lecture 36: Sampling Distribution, Standard Deviation, Test Statistic

• School: University of Calgary
• Department: Statistics
• Course: STAT 213
• Professor: Anatoliy Swishchuk

Document Summary

Large sample con dence interval for a di erence in. Signi cance test for a di erence in proportions. In this way, we have: 2 populations, 2 variables: x1 and x2, in population 1 and population 2, respectively, 2 proportions: p1 and p2 for each population. To compare the two proportions, we use the di erence between the two sample proportions: When both sample sizes are su ciently large, the sampling distribution. D = p1 p2. of the di erence d is approximately normal. The mean of d is the di erence of the means: The addition rule for variances tells us that variance of d is the sum of the variances: P2 = p1(1 p1) n1 p2(1 p2) n2. Therefore, when n1 and n2 are large, d is approximately normal with mean d = p1 p2 and standard deviation. D =! p1(1 p1) n1 p2(1 p2) n2. 2 large sample con dence interval for a dif- ference in proportions.