Confidence Intervals and the Margin of Error
When we take a sample from a population, we use descriptive statistics to summarize that sample data.
However, we can also use sample data to draw conclusions about the population.
Confidence intervals are one way we make inferences about the population.
The CI is an estimate of the range of values within which the population mean is most likely to fall.
https://storage.ning.com/topology/rest/1.0/file/get/2643147846?profile=original
Sample data is collected and used when it is difficult to survey an entire population. We use reliable sample (link sample to populations and sample section 1.a.ii) data to estimate population parameters.
When we hear the term margin of error in news reports, often they are referring to confidence intervals.
https://thehill.com/hilltv/what-americas-thinking/558396-poll-51-percent-support-making-child-tax-credit-fully
How do we calculate the margin of error and CI?
We use sample data to calculate a margin of error, then add and subtract the margin of error from the sample mean to calculate the CI.
Calculating the margin of error (95% confidence level)
Margin of error = E = 1.96s
√n
s = sample standard deviation
n = sample size
Confidence Level |
Value of Z |
95% |
1.96 |
99% |
2.58 |
Interpreting the confidence interval
Applying the central limit theorem (link to section on central limit theorem) we know that:
https://sites.nicholas.duke.edu/statsreview/671-2/
What does this really mean?
We can use the sample data to estimate, with a certain amount of certainty, between which values the population mean lies.