Question

Suppose that 14% of voters in Indian River county support a certain candidate for the school board. Consider the sampling distribution of the sample proportion of supporters with sample size n 174. Determine the mean and standard deviation of the sampling distribution of p. Round solutions to four decimal places, if necessary. What is the mean of this distribution? μₚp=_____ What is the standard error of this distribution? σₚp=________

Answer 1

Firstly, let's find the mean of the sampling distribution of the sample proportion. This is equal to the population proportion, which is 14% or 0.14. Therefore, μₚp= 0.14

Next, we need to calculate the standard error of the sampling distribution. The formula for the standard error (sometimes known as the standard deviation of the sampling distribution of a proportion) is sqrt[p(1 - p) / n].

Here, p represents the population proportion and n is the sample size. In this case, p is 0.14 and n is 174.

We replace p and n in the formula with these values. So,
σₚp = sqrt[(0.14*(1 - 0.14)) / 174]

After carrying out the calculation and rounding to four decimal places, we find that the standard error, σₚp, is 0.0263.

So, the mean of the sampling distribution of the sample proportion μₚp is 0.14 and the standard error of this distribution σₚp is 0.0263.