Question

the aptitude test was administered to random sample of 120 SHS students. the sample mean was 104.2 with standard deviation of 12. find 99% confidence interval

Answer 1

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{s}{\sqrt{n}},$

where:

• $\bar{x}=104.2$ : sample mean
• z: the chosen z-value, for a 99% confidence interval z = 2.576
• $s=12$ :  sample standard deviation
• n = 120:  sample size.

So,

$CI=104.2 \pm 2.576\cdot\cfrac{12}{\sqrt{120}}=\\= 104.2\pm2.82=(101.38, 107.02).$