Question

Determine μ and σ from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate. μ = 61, σ = 10, n = 25 Group of answer choices μ = 12.2, σ = 2 μ = 61, σ = 0.4 μ = 61, σ = 2 μ = 61, σ = 10

Answer 1

Using the given population mean of μ = 61, population standard deviation of σ = 10, and sample size of n = 25, the standard error of the mean (SEM) is calculated as 2. Therefore, the population mean is μ = 61, and the standard deviation for the sample is σ = 2.

Step-by-step explanation:

To determine μ (mu) and σ (sigma) from the given parameters of the population and the sample size, we apply the definitions of these symbols. Here, μ represents the population mean, and σ represents the population standard deviation. In the context of a sample, the standard error of the mean (SEM), which is derived from the standard deviation (σ) and the sample size (ν), is used to describe how much the sample mean is expected to fluctuate around the population mean μ.

The formula for the standard error of the mean (SEM) is:

SEM = σ / √n

Given the population mean μ = 61, the population standard deviation σ = 10, and the sample size n = 25, the standard error of the mean is:

SEM = 10 / √25 = 10 / 5 = 2

Therefore, the population mean remains μ = 61, and using the formula for SEM, we obtain the value of σ for the sample as 2.

The correct answer from the given choices is therefore: μ = 61, σ = 2.