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
2.71 was my answer. .
To find the value of z, we can use the formula for the test statistic of the difference between two proportions:
z = (p1 - p2) / √((p̂ * (1-p̂) / n1) + (p̂ * (1-p̂) / n2))
Where:
p1 and p2 are the proportions of the respective groups,
n1 and n2 are the respective sample sizes, and
p̂ is the combined proportion of both groups.
In this case, p1 is 327/386 = 0.8466, p2 is 321/414 = 0.7754, n1 is 386, and n2 is 414. Now we can calculate p̂:
p̂ = (n1 * p1 + n2 * p2) / (n1 + n2)
p̂ = (386 * 0.8466 + 414 * 0.7754) / (386 + 414)
p̂ = 716.3276 / 800
p̂ ≈ 0.8954
Now we can substitute the values into the formula:
z = (0.8466 - 0.7754) / √((0.8954 * (1-0.8954) / 386) + (0.8954 * (1-0.8954) / 414))
z = 0.0712 / √((0.8954 * 0.1046 / 386) + (0.8954 * 0.1046 / 414))
z = 0.0712 / √(0.09381988 + 0.08655930)
z = 0.0712 / √0.18037918
z ≈ 0.0712 / 0.4249
z ≈ 0.1677
Therefore, the value of z is approximately 0.17, not 2.71.