Question

Suppose 14% of the listeners of a radio station listen to it while they are at work. What is the approximate standard deviation of the sampling distribution of the proportion for the sample of size 85?

Answer 1

To calculate the approximate standard deviation of the sampling distribution of the proportion for a sample size of 85, we can use the formula:

Standard Deviation (σ) = √[(p * (1 - p)) / n]

where:
p is the proportion of listeners (14% or 0.14 in decimal form),
1 - p is the complement of the proportion,
n is the sample size.

Substituting the values into the formula:

σ = √[(0.14 * (1 - 0.14)) / 85]

Calculating this expression gives us the approximate standard deviation of the sampling distribution of the proportion for the given sample size.