Question

question 9
1 pts
a local newspaper reports that, with 95% confidence, the interval from 0.351 to 0.407 includes the proportion of all college students who take advantage of campus printing services. this means the margin of error is equal to what value?
0.014
0.056
0.028
0.379
there is not enough information available in this question to determine the margin of error.
question 10
1 pts
a 90% confidence interval is constructed in order to estimate the proportion of college students who are involved in at least one extracurricular activity. the interval is centered at 0.64, with a margin of error of 0.027. which one of the following intervals must be a 95% confidence interval constructed using the same sample of data?
0.620 to 0.662
0.608 to 0.672
0.611 to 0.669
0.604 to 0.676
0.615 to 0.665

Explanation:

Step1: Recall the formula for margin of error in confidence interval

The formula for a confidence interval for a proportion is \(\hat{p}-E

Step2: Calculate the length of the given confidence interval

Given the confidence interval \((0.351,0.407)\), the length \(L = 0.407-0.351=0.056\).

Step3: Solve for the margin of error \(E\)

Since \(L = 2E\), then \(E=\frac{L}{2}\). Substituting \(L = 0.056\) into the formula, we get \(E=\frac{0.056}{2}=0.028\).

Answer:

\(0.028\) (the third option)