Answer to Question #187117 in Statistics and Probability for Stephanie

Question

Find margin of error and confidence interval for the population mean µ of the college graduates who have taken the statistics course if average value for sample of 25 objects is 52,620 and sample standard deviation S=10,700 . Use 95% confidence interval. (Use t-distribution)

Answer 1

Given, $n=25, \mu=56250,\sigma=10,700$

$\alpha=0.05, t_{\frac{\alpha}{2}}=t_{0.025}=2.064$

Critical value is 2.064.

Margin of Error (MOE)=critical value $\times$ population standard deviation

$=2.064\times \dfrac{10700}{\sqrt{25}}$

$=2.064\times \dfrac{10700}{5}=4416.96$

Confidence Interval $=\mu\pm MOE=52620\pm 4416.96=(48233.04,57066.9)$