Question

A baseball team calls itself “America’s Favorite Team,” because it has 90,000 fans on social media out of 2,210,000 social media users. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=1,000. Round all answers to 3 decimal places.

Answer 1

We are given

x = number of observations of interest = 90,000

n = sample size = 2, 210,000

Population proportion = p = x/n = 90000/2210000 = 0.040724

Population proportion = 0.041

The mean and standard deviation for the sampling distribution of the sample proportion is given as below:

Mean of the sampling distribution of p̂ = p = 0.041

Standard deviation of the sampling distribution of p̂ = sqrt(p*(1 – p)/n)

We are given p = 0.041, n = 1000

Standard deviation of the sampling distribution of p̂ = sqrt(0.041*(1 - 0.041)/1000)

Standard deviation of the sampling distribution of p̂ = 0.00627

Standard deviation of the sampling distribution of p̂ = 0.006