Question

3. A survey is taken of males in a large state University using a SRS. 72% of the 100 males reported that college was easier than high school. Create a 95% confidence interval for the true percentage of males at the University who feel college is easier than high school.
4. 200 single people in the United States 1040s are randomly selected. The mean income of these people is found to be $28,000 with a standard deviation of $40,000. a) Calculate the standard error.b) Find a 95% confidence interval for the mean income of single people in the United States.

Answer 1

$Quiz\ 3\\ CI=\hat {p} \plusmn z_{\alpha/2} \sqrt {\frac{ \hat{p}(1-\hat{p})}{n}}\\ z_{\alpha/2} =1.96\\ CI=0.72 \plusmn 1.96 \sqrt {\frac{ 0.72(0.28)}{100}}\\ CI=0.72 \plusmn 0.088\\ CI: [0.632,0.808]\\ Quiz\ 4\\ a)\ SE=\frac{s}{\sqrt{n}}=\frac{40000}{\sqrt{200}}=2828.427\\ b)\ CI=\bar {x} \plusmn {z_{\alpha/2}} \frac {s}{\sqrt{n}}\\ z_{\alpha/2} =1.96\\ CI=28000 \plusmn {1.96} \frac {40000}{\sqrt{200}}\\ CI=28000 \plusmn 5543.717\\ CI: [22456.283, 33543.717]\\$