Question

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	19	9	7	35
Female	14	8	11	33
Total	33	17	18	68

Let p represent the population proportion of all female students who received a grade of C on this test. Use a 98% confidence interval to estimate p to four decimal places if possible.

Answer 1

sample success x =		11
sample size          n=		33
sample proportion p̂ =x/n=		0.3333
std error se= √(p*(1-p)/n) =		0.0821
for 98 % CI value of z=		2.326
margin of error E=z*std error   =		0.1909
lower bound=p̂ -E                       =		0.1424
Upper bound=p̂ +E                     =		0.5242

from above:

98% confidence interval =(0.1424 , 0.5242)