Question

For a population with standard deviation of 16. how large a

sample is necessary to have a standard error that is less than 3
points

Answer 1

To have a standard error less than 3 for a population with a standard deviation of 16, a sample size of at least 29 is necessary.

Step-by-step explanation:

To determine how large a sample is necessary for the standard error to be less than 3 points for a population with a standard deviation of 16, we use the formula for the standard error (SE) of the mean, which is SE = σ / √n, where σ is the population standard deviation and n is the sample size. We want to find n such that SE < 3.

First, we set up the inequality:

16 / √n < 3

Squaring both sides, we get:

256 / n < 9

Multiplying both sides by n and then dividing by 9, we get:

256 < 9n

Dividing both sides by 9 gives us:

n > 256 / 9

n > 28.44

Since we cannot have a fraction of a sample, we round up to the nearest whole number, which gives us n = 29. Therefore, a sample size of 29 is necessary to have a standard error that is less than 3 points for a population with a standard deviation of 16.