Consider the following data collected in two recent surveys of whether voters in cities A and B favor a ballot proposition in the next election.
City Sample Size In Favor
A 615 463
B 585 403
Suppose you're going to conduct a significance test to see if there's a difference between the two population proportions. What's the standard error of the estimate?
To calculate the standard error of the estimate for the difference between two population proportions, you can follow these steps:
Step 1: Calculate the sample proportions for each city.
- For City A: Sample Proportion (A) = number of voters in favor / sample size = 463 / 615 = 0.754
- For City B: Sample Proportion (B) = number of voters in favor / sample size = 403 / 585 = 0.689
Step 2: Calculate the overall sample proportion.
- Overall Sample Proportion = (number of voters in favor in City A + number of voters in favor in City B) / (sample size of City A + sample size of City B)
- Overall Sample Proportion = (463 + 403) / (615 + 585) = 866 / 1200 = 0.722
Step 3: Calculate the standard error of the estimate.
- Standard Error = sqrt [ (Overall Sample Proportion * (1 - Overall Sample Proportion) * (1 / sample size of City A)) + (Overall Sample Proportion * (1 - Overall Sample Proportion) * (1 / sample size of City B)) ]
- Standard Error = sqrt [ (0.722 * (1 - 0.722) * (1 / 615)) + (0.722 * (1 - 0.722) * (1 / 585)) ]
By performing the calculations, you will get the value for the standard error of the estimate.