Answer to Question #320222 in Statistics and Probability for bae

Question

1. Louie wants to estimate the average value of the lot in his town with 99% confidence interval. Use his random sample of 36 lots with an average value of Php251, 131.42 and a standard deviation of Php1 321.467 to find the confidence interval.

2. A survey conducted for 200 students to determine if they need financial assistance in their studies, it found out that 168 of them needed this assistance. Find the 90% confidence interval for the population proportion of students needing loans or scholarships.

Answer 1

$1:\\\left( \bar{x}-\frac{s}{\sqrt{n}}t_{n-1,\frac{1+\gamma}{2}},\bar{x}+\frac{s}{\sqrt{n}}t_{n-1,\frac{1+\gamma}{2}} \right) =\left( 251131.42-\frac{1321.467}{\sqrt{36}}\cdot 2.7238,251131.42+\frac{1321.467}{\sqrt{36}}\cdot 2.7238 \right) =\\=\left( 250532,251731 \right) \\2:\\\hat{p}=\frac{168}{200}=0.84\\\left( \hat{p}-\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}},\hat{p}+\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}} \right) =\\=\left( 0.84-\sqrt{\frac{0.84\left( 1-0.84 \right)}{200}}\cdot 1.645,0.84+\sqrt{\frac{0.84\left( 1-0.84 \right)}{200}}\cdot 1.645 \right) =\\=\left( 0.797357,0.882643 \right)$