# STAT151 Lecture Notes - Lecture 22: Confidence Interval, Standard Deviation, Sampling Distribution

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## Document Summary

Comparisons between two percentages are much more common than quesions about isolated percentages. We oten want to know how two groups difer, whether a treatment is beter than a placebo control, or whether this year"s results are beter than last year"s. The standard deviaion of the diference between two proporions. In order to examine the diference between two proporions, we need another ruler the standard deviaion of the sampling distribuion model for the diference between two proporions. Recall that standard deviaions don"t add, but variances do. In fact, the variance of the sum or diference of two independent random variables is the sum of their individual variances. So the standard deviaion of sum or diferences of two independent random variables is the square-root of the sum of their individual variances. Proporions observed in independent random samples are independent. The standard deviaion of the diference between two sample proporions is. Thus, the standard error is p 2q 2 n2.

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