Question

Suppose a sample of n=50 items is selected from a population of manufactured products and the weight,X,of each item recorded. Prior experience has shown that the weight has a probability distribution with µ= 6 ounces and σ= 2.5 ounces. Suppose a sample of size 15 is selected, which of the following is TRUE?

a. The standard deviation of the sampling distribution is 2.5 ounces
b. The mean of the sampling distribution is 6 ounces
c. The standard error of the mean is .64 ounces
d. Both a) and c) are correct

Answer 1

The mean of the sampling distribution is the population mean, which is 6 ounces, and the standard error of the mean for a sample size of 15 is approximately 0.64 ounces.

Step-by-step explanation:

The question refers to the sampling distribution of the sample mean. In a sampling distribution:

• The mean of the sampling distribution (the average of all possible sample means) is equal to the population mean (μ).
• The standard deviation of the sampling distribution (also known as the standard error) is equal to the population standard deviation (σ) divided by the square root of the sample size (n).

Given the population mean (μ) is 6 ounces and the standard deviation (σ) is 2.5 ounces, with a sample size of 15, we can calculate the standard error (SE) as:

SE = σ / √n

SE = 2.5 / √15

SE = 2.5 / 3.872983

SE ≈ 0.6455

Hence, the correct answers are b) The mean of the sampling distribution is 6 ounces and c) The standard error of the mean is approximately 0.64 ounces.