Question

A sampling distribution of the mean has a mean μ

x
=57 and a standard error σ
x
=5 based on a random sample of n=10.
a. What is the population mean?

Answer 1

The mean of the sampling distribution is an unbiased estimator for the population mean. Hence, given that the sample mean is 57, the population mean is also 57.

Step-by-step explanation:

The student asks about the population mean given the sampling distribution of the sample mean. For a sampling distribution where the mean (μx) is 57 and the standard error (σx) is 5 based on the sample size (n) of 10, we can infer that the population mean (μ) is also 57. This is because the mean of the sampling distribution (μx) is an unbiased estimator of the population mean (μ).

Additionally, some parts of the provided reference information state formulas and examples but they do not directly provide an answer to the student's question. For a normal distribution and large sample sizes, it's expected that the sampling distribution will approach normality due to the Central Limit Theorem. Furthermore, a reference to confidence intervals also shows how the sample mean can estimate the population mean within a margin of error.