A. Confidence Intervals

Consider the hockey information presented at the beginning of the lesson. The Key Findings stated that 66% of Canadians deem on-ice fights as "not important to hockey". To be entirely sure that 66% of Canadians actually feel this way, Angus Reid Public Opinion would need to ask the entire Canadian population. This would be extremely difficult, time-consuming, and expensive. As such, a sample of the population was asked and the results were generalized (estimated) for the entire Canadian population. The ±3.1% is an indication of how close this estimate is expected to be to the actual feelings of all Canadians; and it represents the margin of error for the group of Canadian adults polled. In other words, for the estimate of 66% of Canadians deeming on-ice fights as "not important to hockey", it is expected that 66% ±3.1%, or between 62.9% and 69.1%, of Canadians felt this way. This range of values is called the confidence interval.

Example 1

Determine the confidence interval for hockey fans that deem on-ice fights as "not important to hockey".

The estimated measure of 67% has a margin of error of ±4.5%.

This means the researcher, Angus Reid Public Opinion, is fairly sure that the percentage of all hockey fans that felt this way was between 62.5% and 71.5%.