Consider two independent random samples with the following results: n1=532x1=390
ID: 3074835 • Letter: C
Question
Consider two independent random samples with the following results:
n1=532x1=390
n2=730x2=139
Use this data to find the 90% confidence interval for the true difference between the population proportions.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2 of 3: Find the margin of error. Round your answer to six decimal places.
Step 3 of 3: Construct the 90% confidence interval. Round your answers to three decimal places.
Explanation / Answer
n1 = 532
x1 = 390
p^1 = 390/532 = 0.733
n2 = 139
x2 = 730
p^2 = 139/730 = 0.190
Step 1 to 3
Here point estimate = p^1 -p^2 = 0.733 - 0.190 = 0.543
Step 2 to 3
Pooled estimate = p = (139 + 390)/ (532 + 730) = 0.4192
margin of error = Critical test statistic * standard error of sample mean
standard error of sample mean = sqrt [0.4192 * (1 - 0.4192) * (1/532 + 1/730)] = 0.0281
Margin of error = 1.645 * 0.0281 = 0.0463
Step 3 of 3
90% confidence interval = 0.543 +- 0.0463 = (0.497, 0.589)