Question

Solve the given problem. Find the following and show your complete solution.

a. Degrees of Freedom

b. Critical Value

c. Confidence Interval

GIVEN:

A sample of six college basketball player had an average weight of 217 pounds with a sample standard deviation of 10 pounds. Find the 95% confidence interval of the true mean weight of all basketball player.

Answer 1

We have a Sample of 6 basketball players,

Mean, $\mu = 217$

Sample standard deviation, $s = 10$

a.) Degrees of freedom = Sample size - 1 $= 6-1 = 5$

b.) Critical value for 95% confidence interval = 1.96

c.)Confidence interval can be calculated using,

$CI = \mu \pm z\dfrac{s}{\sqrt n}$

$= 217 \pm (0.95) \dfrac{10}{\sqrt 6}$

$CI = 217 \pm 3.89$