Question

For a population with σ = 12, how large a sample is necessary to have a standard error that is less than 4 points? n > ?

Answer 1

To have a standard error less than 4 points with a population standard deviation of 12, the necessary sample size must be greater than or equal to 10.

Step-by-step explanation:

To determine the sample size needed to achieve a specific standard error, you can use the formula for standard error of the mean (SEM):

SEM = σ / √n,

where σ is the population standard deviation and n is the sample size. To find the sample size (n) that results in a SEM less than 4 points, given a population standard deviation (σ) of 12 points, rearrange the formula to solve for n:

n = (σ / SEM)2 = (12 / 4)2 = 9.

Since n must be greater than 9 to achieve a standard error less than 4, the smallest integer value for n would be 10. Therefore, the sample size must be greater than or equal to 10.

Answer 2

To have a standard error less than 4 points for a population with sigma = 12, a sample size of at least 9 is necessary.

Step-by-step explanation:

To find the sample size necessary to have a standard error less than 4 points, we can use the formula for standard error: SE = sigma / sqrt(n). Given that sigma = 12 and we want SE < 4, we can solve for n:

4 = 12 / sqrt(n)

Multiplying both sides by sqrt(n) and rearranging the equation, we get:

sqrt(n) = 12 / 4

Simplifying, we have:

sqrt(n) = 3

Squaring both sides gives us:

n = 9

Therefore, a sample size of at least 9 is necessary to have a standard error less than 4 points.