Question

Suppose you are planning an experiment to test the effects of various diets on the weight gain of young turkeys. The observed variable will be gain in three weeks (measured over a period starting one week after hatching and ending three weeks later). Previous experiments suggest that the standard deviation of under a standard diet is approximately 80 g. Using this as a guess of ????????, determine how many turkeys you should have in a treatment group, if you want the standard error of the group mean to be no more than (a) 20 g (b) 15 g

Answer 1

Answer with explanation:

Formula to find the standard error :

$se=\dfrac{\sigma}{\sqrt{n}}$

We are given that , $\sigma=80\ g$

a) Standard error : se= 20 g

Substitute theses values in the above formula , we get

$20=\dfrac{80}{\sqrt{n}}$

$\Rightarrow\ \sqrt{n}=\dfrac{80}{20}=4$

Squaring both sides , we get

$n=(4)^2=16$

Hence, we should have 16 turkeys in a treatment group.

b) Standard error : se = 15 g

Substitute theses values in the above formula , we get

$15=\dfrac{80}{\sqrt{n}}$

$\Rightarrow\ \sqrt{n}=\dfrac{80}{15}$

Squaring both sides , we get

$n=(\dfrac{80}{15})^2=28.444444444\approx29$

Hence, we should have 29 turkeys in a treatment group.