Answer to Question #141071 in Statistics and Probability for Margaret

Question

For a simple random sample of 15 items from a population that is approximately normally distributed with a sample mean X =82 and a sample standard deviation S=20.5. The 95% confidence interval of the population mean is
1. 70.6463 ; 93.3537
2. 721.6789 ; 91,3211
3. 71.6256 ; 92.3744
4. 70.7204 ; 93.2796
5. 70.6463 ;93.3537

Answer 1

Since population standard deviation is unknown, t-distribution is used

$CI=\bar{X}\pm{t_{\frac{\alpha}{2},n-1}}\frac{s}{\sqrt{n}}$

$=82\pm{t_{{0.025,14}}\frac{20.5}{\sqrt{15}}}$

$=82\pm{2.145×\frac{20.5}{\sqrt{15}}}$

$=82\pm{11.35365}$

={70.64635;93.35365}

choice 1 is the correct answer