Determining Sample Size An educator wants to determine the dif...

Question

Determining Sample Size An educator wants to determine the difference between the proportion of males and females who have completed four or more years of college. What sample size should be obtained if she wishes the estimate to be within 2 percentage points with 90% confidence, assuming that
a. she uses the 1999 estimates of 27.5% male and 23.1% female from the U.S. Census Bureau?

a. she uses the 1999 estimates of 27.5% male and 23.1% female from the U.S. Census Bureau?

Accepted Answer

Welcome back everyone. In this problem, a researcher wants to compare the proportion of urban and rural residents who recycle regularly. She wants her estimate of the difference to be within 2% points with a 95% confidence. Prior studies suggest that 35% of urban and 27% of rural residents recycle regularly. What is the minimum sample size she should use for each group? AS 4,0067, B 4,068, C 4,078, and D, 4,087. Now, how can we estimate the minimum sample size required for each group? What do we know? Well, recall, based on the sample sized formula for the difference in proportions, the sample size n would be equal to z2 multiplied by P1 multiplied by 1 minus p 1 plus z squared multiplied by P2. Multiplied by 1 minus P had 2. All divided by E squared. Now if we were to make sense of our variables here, then we could go ahead and solve for N, and we can because so far we know that Z or Z value for our 95% confidence based on our standard normal distribution table is going to be 1.96. Next, we know that PAT one, or we can let, we can set PA 1 to be equal to the estimated proportion for urban residents, 35% or 0.35%. He had two to be the other proportion of rural residents 0.27% or 27% and our margin of error E to be 0.02 because as it says in our problem statement, she wants or her estimate of the difference to be within 2% points. Thus we can use this information to solve for our sample size because no, that means n is going to be equal to 1.96 squared multiplied by 0.35 multiplied by 1 minus 0.35. OK, plus. 1.96 squared multiplied by 0.27 multiplied by 1 minus 0.27. OK. And now all of this is going to be divided by 0.02 squared. And now when we go ahead and solve here, we should get N to be equal to 4,0077.8584. But now remember, we can't have a sample size that has 0.8584. Uh, the sample size must be a whole number, so we would round up to the next integer. So the required sample size N is gonna be equal to 4,0078. This is the minimum sample size for each group of for urban and rural residents. If we look back at our answer choices, that means that uh C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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