At a university, 61% of the 7400 students are female. The student newspaper repo

Question

At a university, 61% of the 7400 students are female. The student newspaper reports results of a survey of a random sample of 50 students about various topics involving alcohol abuse, such as participation in binge drinking. They report that their sample contained 26 females. Gender is a categorical variable. To set up a probability distribution where the random variable X represents gender, Let X = 1 for a female and let X = 0 for a male.

(c) Consider the sampling distribution of the sample proportion of females in samples of size 50. State the mean and standard error for this sampling distribution.

Explanation / Answer

c)

Here,          
n =    50      
p =    0.61      

hence,

u = mean = p =    0.61   [ANSWER, MEAN]

SE = standard error = sqrt(p(1-p)/n) =    0.068978257 [ANSWER, STANDARD ERROR]

************************************

If you use finite population correction, the answer for the standard error would instead be

fpc = sqrt[(N-n)/(N-1)] = sqrt((7400-50)/(7400-1)) = 0.996683241

hence,

SE = standard error = fpc*sqrt(p(1-p)/n) =    0.996683241*0.068978257 = 0.068749473
[ANSWER, STANDARD ERROR]

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