In: Statistics and Probability
Ian is testing to see if Irvinites eat more fruits and vegetables than the average American. Previous research indicates that Irvinites eat 5.8 servings per day. The national average is 4.6 with a standard deviation of three. How many people does Josh need in his sample to achieve a power of .80
True mean, µ = 5.8
hypothesis mean, µo = 4.6
Level of Significance , α =
0.05
std dev = σ = 3
power = 0.8
ß= 1-power = 0.2
δ= µ - µo = 1.2
Z ( α ) = 1.6449 [excel
function: =normsinv(α)
Z (ß) = 0.8416 [excel
function: =normsinv(ß)
sample size needed = n = ( ( Z(ß)+Z(α) )*σ / δ )² = (
( 0.8416 + 1.6449 )
* 3.0 / 1.2 ) ²
= 38.6410
so, sample size =
39