Answer to Question #269023 in Statistics and Probability for zaqwan

Question

The mean weight (in kg) for 8 adults males are given as follows: 70 72 65 80 75 76 68 78 Construct a 90% confidence interval estimate for the mean weight for all adult males. 

Answer 1

$\bar x=\frac{70+72+65+80+75+76+68+78}{8}=\frac{584}{8}=73.$

$s=\sqrt{\frac{70^2+72^2+65^2+80^2+75^2+76^2+68^2+78^2-8*73^2}{7}}=5.1547.$

$90\%CI=(\bar x-t_{0.05,n-1}\frac{s}{\sqrt{n}},\bar x+t_{0.05,n-1}\frac{s}{\sqrt{n}})=$

$=(73-1.8946\frac{5.1547}{\sqrt{8}},73+1.8946\frac{5.1547}{\sqrt{8}})=(69.5472,76.4528).$