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

The population proportion is 0.041.

Step-by-step explanation:

To find the population proportion, you divide the number of fans by the total number of social media users: 90,000 / 2,210,000 = 0.041 (rounded to 3 decimal places).

The mean (μ) of the sampling distribution for sample proportions is equal to the population proportion, so in this case, the mean is also 0.041.

The standard deviation (σ) of the sampling distribution for sample proportions is calculated using the formula σ = sqrt[(p * (1 - p)) / n], where p is the population proportion and n is the sample size. Substituting the values, we get σ = sqrt[(0.041 * (1 - 0.041)) / 1,000] ≈ 0.006.

Therefore, the population proportion is 0.041, the mean is 0.041, and the standard deviation is approximately 0.006 (all rounded to 3 decimal places).