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

To construct a 90% confidence interval, firstly needs to determine mean and standard deviation using weight (in kg) for 8 adults males.

Mean:

$\bar{x}=\frac{\Sigma X}{N}=\frac{(70+72+65+80+75+76+68+78)}{8}=73$

Standard deviation:

$s=\sqrt{\frac{\Sigma (x-\bar{x})^2}{n-1}}$

$s=\sqrt{\frac{(70-73)^2+(72-73)^2+(65-73)^2+(80-73)^2+(75-73)^2+(76-73)^2+(68-73)^2+(78-73)^2}{8-1}}$

$s=\sqrt{\frac{ (9+1+64+49+4+9+25+25}{7}}$

$s=5.15$

z value at 90% confidence interval = 1.645

Following is the equation for 90% confidence interval:

$CI=\bar{x}\pm z\frac{s}{\sqrt{n}}$

$CI=73\pm 1.645\times\frac{5.15}{\sqrt{8}}$

$CI=73\pm 3$

90% confidence interval = (70, 76)