Confidence intervals 1: Theory

Question 1

Define a confidence interval

Answer 1

An interval (i.e. a range) of values for
our population parameter, together with a specified level of confidence that
the parameter is in that range

Simply = If we repeat our data collection many times, we are confident that 95% of the time, our data range falls within the population parameter

Question 2

What is the formula for 95% CI?

Answer 2

mean - (1.96 x SDM SD)
mean + (1.96 x SDM SD)

Question 3

What is the main rule for a 95% CI?

Answer 3

The 95% CI for the population mean is centred on the sample mean m and goes from
m - (1.96 x s/√N) to m + (1.96 x s/√N)

Question 4

What does a 95% confidence level mean?

Answer 4

If we repeated our sampling many times
and worked out a new CI each time that was centred on our new sample mean, we
would expect the population mean to be in that interval on 95% of repeats

Question 5

A Confidence Interval provides an interval estimate for a population parameter and also specifies a level of confidence that the population parameter is in that range.

1) True
2) False

Answer 5

True

Question 6

Fill in the blank:

A 95% confidence interval specifies (……) for a (……..)

Answer 6

1) An interval estimate
2) Population parameter

Question 7

Having a 95% confidence interval for a population mean centred on a sample mean for a sample of size N …..

a. Means that there is a 95% probability that the confidence interval contains the population mean

b. Does not mean that there is a 95% probability that the confidence interval contains the population mean

Answer 7

B