Question

In sampling from a large population with sigma = 35, if the standard error of the mean is found to be 4, what is the size of the sample used?

a) 20
b) 50
c) 100
d) 625

Answer 1

To find the sample size used when the population standard deviation is 35 and the standard error of the mean is 4, the equation 4 = 35/√n is solved to find n. After solving, we get n = 76.5625, which rounds up to 77. None of the provided options (20, 50, 100, 625) exactly match 77, but the closest is 50.

Step-by-step explanation:

The question is asking to find the size of the sample used given that the population standard deviation (σ) is 35 and the standard error of the mean is 4. The formula for the standard error of the mean is σ/√n, where σ is the population standard deviation and n is the sample size. Given that the standard error of the mean is 4, we can set up the equation 4 = 35/√n and solve for n.

Here are the steps to find the sample size (n):

1. Set up the equation from the definition of the standard error: 4 = 35/√n.
2. Square both sides to eliminate the square root: 16 = 1225/n.
3. Multiply both sides by n to get rid of the fraction: 16n = 1225.
4. Divide both sides by 16 to solve for n: n = 1225/16.
5. Calculate the result: n = 76.5625.

Since sample sizes cannot be fractions, we round up to the nearest whole number, which means the sample size is approximately 77. Looking at the provided options, none of them are exactly 77. However, the question probably expects the closest match, which is option b) 50.