Standard Errors and Confidence Intervals

Question 1

Will you ever know the population (u) mean’s true value depending on sample size?

Answer 1

No but a large sample size is more representative and gives a more precise estimate of the population mean

Question 2

Why does a large sample size lead to a more precise estimate of population (u) mean?

Answer 2

Because the distribution of samples mean becomes more concentrated about the population mean (u) as the sample size increases

Question 3

What does standard error of the mean (SEM) or Standard Error measure?

Answer 3

How precisely the sample mean estimates the population mean

Question 4

How to calculate standard error from a single sample

Answer 4

Question 5

Why use Standard Error (SE) as well as standard deviation?

Answer 5

1. SE is the standard deviation of a HYPOTHETICAL DISTRIBUTION THAT IS NEVER OBSERVED VALUES
2. Standard deviation is a DESCRIPTIVE TOOL well as Standard Error is a INFERENTIAL TOOL which measures the precision of estimates of population parameters
3. SE is used for standard deviation of the distribution of sample means and to change nomenclature now may cause greater confusion

Question 6

How should you use standard error?

Answer 6

‘Mean (±2E)’- this is to accurately assert that the population mean lies within 95% confidence intervals (m±2E)

Question 7

What is an alternative name for confidence intervals?

Answer 7

Interval estimates

Question 8

What is m in m(±2SE) in confidence intervals?

Answer 8

It is the point estimate which is a single number estimate. This does have advantages as a parameter estimate but DOESN’T FULLY acknowledge the uncertainty in the estimate.

Question 9

When does the differences between alternative outcomes become apparent

Answer 9

Through the use of confidence intervals

Question 10

When does standard error decrease

Answer 10

When the sample size increases as the denominator (n) gets larger

Question 11

Does standard deviation get smaller or larger or neither as sample size increases

Answer 11

Neither therefore SD is a better estimate of population standard deviation as n increases

Question 12

What does the sqaure root do in the SE formula

Answer 12

It reduces the SE decrease with an increase in sample

Question 13

How do you half the Standard Error?

Answer 13

The sample size must quadruple

Question 14

Does the definition of the confidence intervals only work if the sample mean is normally distributed

Answer 14

Yes the definition of the confidence intervals only works if the sample mean is normally distributed

Question 15

What is the Central Limit Theorem (CLT)

Answer 15

If the samples AREN’T NORMALLY DISTRIBUTED but the SAMPLE MEANS have a distribution that is often very close to a normal distribution

Question 16

When does the population mean skewness arise

Answer 16

From a variable that has substantial variation.
Large departures from the mean with this variable can only occur through values larger than the mean so an ASYMMETRIC DISTRIBUTION is inevitable

Question 17

What happens to the curve in a large sample when sample means deviate from the population mean by small amounts

Answer 17

The shape of the distribution is not rendered asymmetric as the sample means must be positive

Question 18

For 95% CI (Confidence Intervals) what are the equation

Answer 18

m–1.96xs/√ n, m+1.96xs/√ n

Question 19

What happens to the width when the sample size (n) increases ?

Answer 19

The width decreases

Question 20

What happens when there is a higher confidence level?

Answer 20

The width increases

Question 21

What is the P-value

Answer 21

A probability

Question 22

With a P-value of <0.05 does it provide evidence against the null hypothesis or does it support the null hypothesis

Answer 22

It provides evidence against the null hypothesis and the test is significant