There were approximately 28 million adults on Canada when a survey was conducted. In an online survey, 1008 Canadians took part. 68% said that the penny should be abolished. If the margin of error was +- 3.1%, give an upper and lower estimate for the number of Canadian adults that would agree that the penny should be taken out of circulation.
Add up the 28 million and 1008 (i that is what the +- 3.1% refers to) and then find 2 numbers one that is +3.1% of that total and the other is -3.1%.
To estimate the number of Canadian adults who agree that the penny should be abolished, we can use the proportion of respondents in the survey who expressed that opinion.
First, we need to find the upper and lower limits of the confidence interval, given a margin of error of ±3.1%. The margin of error represents the maximum amount by which the estimate could deviate from the true population value.
To calculate the upper and lower estimates, we can use the formula:
Upper Estimate = Proportion + (Margin of Error)
Lower Estimate = Proportion - (Margin of Error)
Given that 68% of the 1008 participants in the survey said the penny should be abolished, the proportion of Canadians in the population who hold that opinion is 0.68.
Upper Estimate = 0.68 + (0.031)
Lower Estimate = 0.68 - (0.031)
Calculating the upper and lower estimates:
Upper Estimate = 0.711
Lower Estimate = 0.649
Now, to estimate the number of Canadian adults who agree that the penny should be taken out of circulation, we can multiply these proportions by the total number of Canadian adults.
Upper Estimate = 0.711 * 28,000,000
Lower Estimate = 0.649 * 28,000,000
Calculating the upper and lower estimate:
Upper Estimate ≈ 19,908,000
Lower Estimate ≈ 18,172,000
Therefore, based on the survey results and the provided margin of error, we can estimate that between approximately 18,172,000 and 19,908,000 Canadian adults would agree that the penny should be taken out of circulation.