Question

5. Describe what we know about the theoretical distribution of sample means. Be sure to

include answers to the questions that follow:



What is a distribution of sample means? How is this different from the

distributions we have been working with up through Chapter 6?



According to the Central Limit Theorem, what three things do we know about

the theoretical distribution of sample means?



Define standard error.



In your own words, what does standard error tell us and why do we need this

information?



How is standard error different from standard deviation?

Answer 1

Q2. According to the Central Limit Theorem, what three things do we know about

the theoretical distribution of sample means?

1.Central Limit Theorem with a Normal Population.

2.Central Limit Theorem with a Dichotomous Outcome.

3. Central Limit Theorem with a Skewed Distribution.

Q3.Define standard error.

a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates.

Q4.

In your own words, what does standard error tell us and why do we need this

information?

Standard Error is a measure of the deviation of the sample means from the population. It helps to decide whether a particular sample, taken out of a population truly belongs to that population. This is done to confirm that the sample taken out of the population represents the population convincingly.

Q5. How is standard error different from standard deviation?

Standard deviation (SD)

This describes the spread of values in the sample. The sample standard deviation, s, is a random quantity -- it varies from sample to sample -- but it stays the same on average when the sample size increases.

Standard error of the mean (SE)

This is the standard deviation of the sample mean, , and describes its accuracy as an estimate of the population mean, . When the sample size increases, the estimator is based on more information and becomes more accurate, so its standard error decreases.

The SEM is always smaller than the SD