The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?
A. 2
B. 3
C. 4
D. 4.1
answer B
To answer this question, we need to know the relationship between the standard deviation of the population and the standard deviation of the distribution of sample means.
The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated by dividing the standard deviation of the population by the square root of the sample size.
In this case, we are given the standard deviation of the population, which is 9. We are also given the sample size, which is 9. To calculate the standard deviation of the distribution of sample means, we divide the standard deviation of the population by the square root of the sample size.
So, the standard deviation of the distribution of sample means is:
Standard deviation of the distribution of sample means = standard deviation of the population / square root of the sample size
Plugging in the values, we get:
Standard deviation of the distribution of sample means = 9 / √9
Simplifying further, we get:
Standard deviation of the distribution of sample means = 9 / 3
Which equals:
Standard deviation of the distribution of sample means = 3
Therefore, the correct answer is B. 3.