Answer to Question #318083 in Statistics and Probability for Owen

Question

Clarendon College claims that some of their BSEd first year students shifted to another course because of their retention policy, which is normally distributed. A random sample of 200 students revealed that 55 of them shifted to another course after their first year.

1. Compute the proportion estimate of the parameter.

2. Compute the standard error of the proportion.

3. Compute the margin of error of the proportion at 90% confidence level.

4. Find 95% confidence interval for all the BSED students shifted to another course after their first year because of the retention policy.

Answer 1

$1:\\\hat{p}=\frac{55}{200}=0.275\\2:\\s=\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}=\sqrt{\frac{0.275\cdot 0.725}{200}}=0.0315733\\3:\\E=\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}}=0.0315733\cdot 1.645=0.0519381\\4:\\\left( \hat{p}-\sqrt{\frac{\hat{p}\left( 1-\hat{p} \right)}{n}}z_{\frac{1+\gamma}{2}} \right) =\left( 0.275-\sqrt{\frac{0.275\cdot 0.725}{200}}\cdot 1.96,0.275+\sqrt{\frac{0.275\cdot 0.725}{200}}\cdot 1.96 \right) =\\=\left( 0.213116,0.336884 \right)$