Question

During a weekend music festival, surveys are taken from a sample size of 40 people on their age. The sample proportion of people in their 40s compared to everyone is found. What is the distribution of the sample proportion?

A.
normal distribution skewed to the right

B.
not a normal distribution

C.
normal distribution

D.
normal distribution skewed to the left

Answer 1

C.

normal distribution

Explanation:

The Sampling Distribution of the Sample Proportion. If repeated random samples of a given size n are taken from a population of values for a categorical variable, where the proportion in the category of interest is p, then the mean of all sample proportions (p-hat) is the population proportion (p)

Sample proportion would be normal with mean = p and variance = pq/n where q = 1-p and n= the sample size

The condition is that both np and nq must be greater than 10

Hence we can take that this will be normal provided np>10 or p>1/4 and q >1/4

i.e. p lies between 1/4 and 3/4

C.

normal distribution (assuming conditions are satisfied)