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 386 327
H 414 321
.
Which one is n , x
Sample n x
G 386 327
H 414 321
Sorry it keeps going together
Samples are G & H
N =386, 414
X =327, 321
n1 = 386
n1 = 414
x1 = 327
x2 = 321
phat1= x1/n2 = 327/386 = .847
phat2 = x2/n2 = 321/414 = .775
Pbar = (x1+x2) /(n1 + n2) = (327+ 321)/(386+414)
pbar = .81
qbar = 1- pbar = .19
z = (phat1-phat2)/(sqrt(pbar *qbar/n1 + pbar *qbar/n2)
z = (.847-775)/(sqrt (.81*.19/386 + .81*.19/414))
z = .072/.02776 = 2.59
To find the value of z for testing the difference between the proportions of two samples, we can follow these steps:
Step 1: Calculate the proportions for each sample.
For sample G:
Proportion_G = x_G / n_G = 327 / 386 ≈ 0.847
For sample H:
Proportion_H = x_H / n_H = 321 / 414 ≈ 0.775
Step 2: Calculate the standard error for the difference between two proportions.
Standard Error = √[(Proportion_G * (1 - Proportion_G) / n_G) + (Proportion_H * (1 - Proportion_H) / n_H)]
Standard Error = √[(0.847 * (1 - 0.847) / 386) + (0.775 * (1 - 0.775) / 414)]
Standard Error ≈ 0.0269
Step 3: Calculate the observed difference between the proportions.
Observed Difference = Proportion_G - Proportion_H
Observed Difference ≈ 0.847 - 0.775 ≈ 0.072
Step 4: Calculate the z-score.
z = (Observed Difference - Hypothesized Difference) / Standard Error
Since the problem didn't provide a hypothesized difference, we assume the null hypothesis as the difference being equal to zero.
z = (0.072 - 0) / 0.0269 ≈ 2.677
Therefore, the value of z used to test the difference between the proportions is approximately 2.677.