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## Statistics and probability

### Course: Statistics and probability>Unit 13

Lesson 1: Comparing two proportions

# Comparing population proportions 1

Sal uses an election example to compare population proportions. Created by Sal Khan.

## Want to join the conversation?

• I have a question about how Sal derived the variance for the men and women groups, starting at or so of this video. It seems that he takes the formula for variance in bernoulli distribution for populations and uses that to calculate the sampling distribution variance. Since you have data from the sample itself, why wouldn't you calculate the sample's variance first (i.e., s^2), then use s^2? It seems like this was done in an earlier video for bernoulli distributions? I thought it would work something like this for the men's sample: s^2=(358x(0-.358)^2)+(642x(.642-0)^2)/1000-1. ... I think that the video showing this was entitled, "Estimating Population Proportion," Any thoughts on this greatly appreciated!
• At about Sal put an n in the sampling distribution for the women, but we already know that it is 1000, correct? We put that number in on the men's side. Help, I'm trying not to get confused!!!!! lol...
• Yes, n=1,000 for the women as well; it's corrected in the next video when it comes time to calculate it.
• A bit confused as to why variance of p1 - p2 is the sum of variance(p1) and variance(p2)?
• Why are you using p-bar and not p-hat? Please help, I am very confused by this. Also why are we not using x-bar?
• Are the male and female voters populations or sample of populations? Note, we do not use the unbiased formula for the standard deviation. And and in later videos in this series, we do not use the standard error of the mean formula.
• when we take 2.5 % of alpha
if our z value is more than 1.96 (but less than 5%) than we reject null hypothesis
(1 vote)
• using 1.96, you put the 95% in the middle section of the normal distribution, and you have 5% left over, 2.5% in each tail. For 95% confidence, alpha is 0.05, but alpha/2 = 0.025. To use some of the typical normal dist tables, you have to look up the probability from a z-value down to negative infinity, so you are looking up the probability 0.95 + 0.025 (the lower tail probability), and that will give you z=1.96. It is still the 95% confidence level, but you have to work with how the z-table is constructed.