Find the value of z that would be used to test the difference between the proportions, given the following. (Use G - H. Give your answer correct to two decimal places.)
Sample n x
G n=384 x=314
H n=423 x=329
To find the value of z that would be used to test the difference between the proportions G and H, we can use the formula:
z = (p1 - p2) / √[ (p1*(1-p1)/n1) + (p2*(1-p2)/n2) ]
Where:
p1 = proportion for G = x/n for G = 314/384 ≈ 0.8177
p2 = proportion for H = x/n for H = 329/423 ≈ 0.7771
n1 = number of observations for G = 384
n2 = number of observations for H = 423
Now, let's substitute these values into the formula to calculate z:
z = (0.8177 - 0.7771) / √[ (0.8177*(1-0.8177)/384) + (0.7771*(1-0.7771)/423) ]
Calculating the expression inside the square root:
z = (0.8177 - 0.7771) / √[ (0.8177*0.1823/384) + (0.7771*0.2229/423) ]
z = (0.8177 - 0.7771) / √[ 0.00172157 + 0.00163062 ]
z = 0.0406 / √[ 0.00335219 ]
z = 0.0406 / 0.05788748
z ≈ 0.701.
Therefore, the value of z to test the difference between proportions G and H is approximately 0.701 when rounded to two decimal places.