Question

1. a population of data, which is unimodal and fairly symmetric, has a mean (μ) and a standard deviation (σ). if samples of size n are randomly chosen from this population, what does the mean of the sample means equal?

sample mean
sample mean divided by the square root of n
population mean
population mean divided by the square root of n

1. a population of data, which is unimodal and fairly symmetric, has a mean (μ) and a standard deviation (σ). if samples of size n are randomly chosen from this population, what does the standard deviation of the sample means equal?

sample standard deviation
sample standard deviation divided by the square root of n
population standard deviation
population standard deviation divided by the square root of n

Explanation:

1. Mean of the sample means

According to the Central Limit Theorem, when samples of size \(n\) are randomly chosen from a population (regardless of the population distribution, as long as the population has a mean \(\mu\) and a standard deviation \(\sigma\)), the mean of the sampling distribution of the sample means \(\mu_{\bar{x}}\) is equal to the population mean \(\mu\).

2. Standard deviation of the sample means

The standard deviation of the sampling distribution of the sample means (also known as the standard error) is given by the formula \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Answer:

1. population mean
2. population standard deviation divided by the square root of \(n\)