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 375 324
H 414 333
Sample n x
G 375 324
H 414 333
n1 = 375
x1 = 324
p1 = x1/n1 = 324/375 = .864
n2 = 414
x2 = 333
p2 = x2/n2= 333/414 = .804
z = 2.24
p-value = .025
Thanks!!
To find the value of z that would be used to test the difference between the proportions, we need to calculate the standard error of the difference in proportions and then use it to find the z-score.
Step 1: Calculate the proportion (p) for each sample:
For sample G: pG = xG / nG = 324 / 375 = 0.864
For sample H: pH = xH / nH = 333 / 414 = 0.804
Step 2: Calculate the standard error of the difference in proportions:
SE = √[(pG * (1 - pG) / nG) + (pH * (1 - pH) / nH)]
= √[(0.864 * (1 - 0.864) / 375) + (0.804 * (1 - 0.804) / 414)]
= √[(0.864 * 0.136 / 375) + (0.804 * 0.196 / 414)]
= √[0.00312 + 0.00384]
= √0.00696
≈ 0.0834
Step 3: Calculate the difference in proportions:
pG - pH = 0.864 - 0.804 = 0.060
Step 4: Calculate the z-score:
z = (pG - pH) / SE
= 0.060 / 0.0834
≈ 0.719
Therefore, the value of z that would be used to test the difference between the proportions is approximately 0.719.