Question

question 5
a survey of a random sample of 1,500 young americans found that 87% had earned their high school diploma. based on these results, the 95% confidence interval for the proportion of young americans who have earned their high school diploma is (0.853,0.887) what is the margin of error for this confidence interval?
a. 0.95
b. 0.034
c. 0.87
d. 0.017
question 6
assuming data come from a random sample, under which of the following conditions should we not calculate a confidence interval for a population mean?
a. population is normally distributed and sample size is 50 individuals.

Explanation:

Step1: Recall margin - of - error formula for proportion

The formula for a confidence interval for a proportion is $\hat{p}\pm E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error. Given the confidence interval $(L, U)$ (lower limit $L$ and upper limit $U$), the margin of error $E=\frac{U - L}{2}$.

Step2: Identify lower and upper limits

Here, $L = 0.853$ and $U=0.887$.

Step3: Calculate margin of error

$E=\frac{0.887 - 0.853}{2}=\frac{0.034}{2}=0.017$

Answer:

D. 0.017