Just one step missing - Hypothesis testing: In 2000 20% of the US adult population...

gazeemyth

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May 8, 2017
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Doing practice test questions and encountered the following problem:

[h=3]In 2000 20% of the US adult population had a college degree. IN 2010, a survey of 850 US adults found that 204 of the adults surveyed had a college degree. Use a 5% significance level to test the hypothesis that the proportion of US adults with a college degree increased from 2000 to 2010.

From here, the known data I was able to get from this is as follows:
Claim: (if P1 represents population in 2000 and P2 represents population in 2010) P1<P2 or P1-P2<0. Null Hypothesis: P1-P2=0. Alternate Hypothesis: P1-P2<0.
Alpha=0.05
So I understand the general process to test the hypothesis, the step I am missing, and can't figure out, is getting the population sample size for the 2000 survey (which I will represent with n1). I remember from an earlier chapter there was a way of determining how big a sample size for a given survey should be, but I can't seem to locate it in my notes, and I have been coming up on dead ends everywhere I turn. The rest of the problem makes sense to me, once I find that sample size finding the amount of people with college degrees in 2000 is just multiplying the n value to .20. With sample size represented by n, number of people who meet criteria listed as x, and proportion listed as p-hat (and all values listed with 1 following to correspond with 2000 and 2 to correspond with 2010), I would then take (X1+X2)/(N1+N2) to get the pooled proportion, take 1-pooled proportion for q value, and then take p(hat)1-p(hat)2/(Square Root of pooled proportion*q/n1+pooled proportion*q/n2), take that value as z, and run a left-tailed normalCDF check, with the result being the P-Value. If the P-value is less than alpha I would reject the null hypothesis and support the claim, and if its greater than alpha, I would fail to reject the null hypothesis with not enough evidence to support the claim.

The only problem I am having in this equation is figuring out how big the sample size should be for the 2000 population.[/h]
 

ktbernoulli

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May 9, 2017
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If proportion is given,

we can totally assume that n1 = 100 for easy sake & x1 = 20 to fulfill the 20% proportion information.
 
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