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.
(a) Show the population distribution of gender at this university. (Use two decimal places.)
Gender X Probability
Female 1
Male 0
(b) Show the data distribution of gender for this sample. (Use two decimal places.)
Gender X Proportion
Female 1
Male 0
(c) Consider the sampling distribution of the sample proportion of females in a sample of size 50. State its mean and standard error.