According to one pollster, 48% of people are afraid of flying. Suppose that a sample of size 20 is drawn. Find the value of standard error , the standard deviation of the distribution of sample proportions.
Write only a number as your answer. Round to two decimal places (for example: 8.21).
To find the standard error, the first step is to calculate the standard deviation of the distribution of sample proportions.
The formula for calculating the standard deviation of the sample proportions (σp) is:
σp = √(p * (1 - p) / n)
where p is the population proportion (in this case, 48% or 0.48), and n is the sample size (20).
Now we can substitute the values into the formula:
σp = √(0.48 * (1 - 0.48) / 20)
Calculating this expression, we get:
σp = √(0.48 * 0.52 / 20)
= √(0.2496 / 20)
= √0.01248
≈ 0.112
Therefore, the value of the standard error, rounded to two decimal places, is approximately 0.11.