Question

46 % of the 100 students in Emmie Xi Hem International School students said that they had been late in their first period classes. What is the lower bound of the 99% confidence interval for the proportion of students in the said school who had been late in their first period classes.

Note: Write your answers in decimal form and round it to 4 decimal places.

Answer 1

Confidence intervals for a proportion are calculated using the following formula:

$\hat{p} \pm Z_{\alpha/2} \sqrt{\cfrac{\hat{p}(1-\hat{p}) } {n} }$

The lower bound: 

$\hat{p} - Z_{\alpha/2} \sqrt{\cfrac{\hat{p}(1-\hat{p}) } {n} }$

$\hat{p}=0.46-$ the sample proportion,

$n=100-$ the sample size,

for 99% confidence interval $Z_{\alpha/2} =2.576,$

$\hat{p} - Z_{\alpha/2} \sqrt{\cfrac{\hat{p}(1-\hat{p}) } {n} } =\\ =0.46 - 2.576\sqrt{\cfrac{0.46(1-0.46) } {100} } =\\ =0.3316.$