Question

A poll is conducted in which randomly sampled Canadian voters are asked, “Do you approve of how Trudeau is handling the current trade dispute with the US?”. According to the results, 72% of respondents replied “yes”. This figure is reported to be accurate to within plus or minus 3.5 percentage points, 19 times out of 20. Explain the sentence written in bold.

Answer 1

Here, our population parameter is the approval percentage. 19 times out of 10 means 95% and within plus or minus 3.5% points means that a confidence interval is being described here.

Now, lower limit of the confidence interval = (72 – 3.5)% = 68.5% and upper limit of the confidence interval of the confidence interval = (72 + 3.5)% = 75.5%.

This means that the sentence written in bold is stating that the 95% confidence interval of the approval percentage is [68.5%, 75.5%]. This further means that if repeated samples are taken and 95% confidence intervals are computed for each of these samples, 95% of these intervals would contain the actual approval percentage value.