R code: UCB <- structure(c(1198, 1493, 2691, 557, 1278, 1835, 1755, 2771, 4526 )
ID: 3302655 • Letter: R
Question
R code:
UCB <-
structure(c(1198, 1493, 2691, 557, 1278, 1835, 1755, 2771, 4526
), .Dim = c(3L, 3L), .Dimnames = structure(list(Admit = c("Admitted",
"Rejected", "Sum"), Gender = c("Male", "Female", "Sum")), .Names = c("Admit",
"Gender")), class = c("table", "matrix"))
Using the UCB data.frame, use the normal approximation and compute the approximate standard error for the proportion of women who were admitted.
Using the UCB data.frame, compute the normal approximation score test statistic (z) to test the hypothesis that the true proportion of men admitted is 0.5 versus that the true proportion differs from 0.5.
Explanation / Answer
Gender
Admit Male Female Sum
Admitted 1198 557 1755
Rejected 1493 1278 2771
Sum 2691 1835 4526
1) standard error = sqrt(np*(1-p))
n = 1755 , X = 557
p =X/n = 557/1755
= 0.3173789
hence
standard error = sqrt(pq/n) =
sqrt(0.3173789*(1-0.3173789)/1755)
= 0.01111067
b) Z = (p^ -p)/se (p^)
= (1198/1755 - 0.5)/0.01111067
=16.43655
since Z > critical values( say 1.96 at alpha = 0.05)
we reject the null
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