Statistics - Confidence Intervals

Question 1

Why is a confidence interval about a point estimate reported?

Answer 1

A point estimate may be the mean

The confidence interval demonstrates how accurate this value may be

Question 2

What is a sample mean used as an estimate of?

Answer 2

The true population mean

Question 3

What is the standard error for the mean used to measure?

Answer 3

The confidence interval of a mean

The spread of the sample mean, NOT the spread of the actual measurements

Question 4

What is the calculation for standard error?

Answer 4

se = sd/(square root n)

the standard deviation of the population is divided by the square root of the sample size

Question 5

How does the standard error tend to change as sample size increases?

Answer 5

The standard error is reduced as sample size increases

Question 6

what is a confidence interval used to specify?

Answer 6

it specifies a range of values (an interval) within which the true population mean is likely to lie

Question 7

What is a necessary step needed to specify confidence intervals?

Answer 7

It is necessary to look up critical values from a normal distribution

Question 8

what are the 2 cases that must be considered when calculating a confidence interval?

Answer 8

1. when sd is known, or is estimated from a sample with 200 or more observations
2. when sd has been estimated from a sample with less than 200 observations

Question 9

How is a confidence interval for the mean calculated when sd for a population is known, or estimated from a sample of 200 or more observations?

Answer 9

It can be calculated using critical values from the standard normal distribution

Question 10

In a population with known standard deviation, what is the best estimate for true population mean?

What confidence interval would be used?

Answer 10

the sample mean

A 95% confidence interval, which is constructed using the standard error of the mean

Question 11

How can the 95% confidence interval be interpreted?

Answer 11

If a study was repeated many times, 95% of the times this interval will include the true population mean

Question 12

What is the most important role of a confidence interval?

Answer 12

It gives a feasible range of values within which the true population might lie

Question 13

If the population standard deviation is not known, how may it be calculated?

Answer 13

It can be estimated from a small sample of less than 200 observations

Question 14

How do the critical values used to construct the confidence interval vary in small samples?

Answer 14

The critical values are a little bit larger

Question 15

what is used opposed to the standard normal distribution in smaller samples?

Answer 15

Student’s t-test distribution for 95% confidence intervals

Question 16

How are degrees of freedom calculated?

Answer 16

One less than the sample size

n-1

Question 17

For large values (sample size over 200) of the number of degrees of freedom, what is the critical value?

Why?

Answer 17

t = 1.96

This is the same as the normal critical value

For large sample sizes, sd is estimated well and the situation is similar to when sd is known

Question 18

Using the standard normal distribution, between which values do 95% of the distribution lie?

How does this give rise to critical values?

Answer 18

95% of the distribution lies between z=-1.96 and z=1.96

The critical values to calculate a confidence interval are z = -1.96 and z = 1.96

Question 19

Why is the Student’s t-test most often used to calculate the 95% confidence interval?

Answer 19

Usually, standard error is calculated from the sample

Standard error is not usually previously known

Question 20

What are the steps used to calculate the 95% confidence interval?

Answer 20

1. determine sample size and degrees of freedom
2. calculate mean and standard deviation
3. calculate standard error
4. look up critical value t in the table
5. work out 95% confidence interval by:

[(mean - t) x (se)] , [(mean + t) x (se)]