Answer to Question #321391 in Statistics and Probability for rose

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,

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