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.
To calculate the upper and lower estimate for the number of Canadian adults that would agree that the penny should be taken out of circulation, we can use the percentage of participants in the survey who agreed (68%) and the margin of error (+-3.1%).
Upper Estimate:
Add the margin of error to the percentage who agreed: 68% + 3.1% = 71.1%
Multiply the total number of Canadian adults (28 million) by this percentage: 0.711 * 28,000,000 = 19,908,000
Lower estimate:
Subtract the margin of error from the percentage who agreed: 68% - 3.1% = 64.9%
Multiply the total number of Canadian adults (28 million) by this percentage: 0.649 * 28,000,000 = 18,172,000
So, the upper estimate is 19,908,000 and the lower estimate is 18,172,000.
To calculate the upper and lower estimates, we need to consider the margin of error. The margin of error is ±3.1%.
First, we can calculate the number of Canadians who said that the penny should be abolished:
Total participants in the survey: 1008
Percentage who said the penny should be abolished: 68%
Number of Canadians who said the penny should be abolished = (68/100) * 1008
= 686.4 (rounded to the nearest whole number)
Next, we'll calculate the upper and lower estimates using the margin of error:
Upper estimate = Number of Canadians who said the penny should be abolished + (Margin of error * Total participants)
= 686 + (0.031 * 1008)
= 686 + 31.248
= 717.248 (rounded to the nearest whole number)
= 717
Lower estimate = Number of Canadians who said the penny should be abolished - (Margin of error * Total participants)
= 686 - (0.031 * 1008)
= 686 - 31.248
= 654.752 (rounded to the nearest whole number)
= 655
Therefore, the upper estimate for the number of Canadian adults who would agree that the penny should be taken out of circulation is 717, and the lower estimate is 655.
To calculate the upper and lower estimate, we'll need to use the proportion of Canadians who said the penny should be abolished.
First, let's calculate the estimated number of Canadian adults who agree that the penny should be taken out of circulation:
Estimated Number = Proportion × Total Number of Adults
Estimated Number = 0.68 × 28 million
Estimated Number = 19.04 million
Now let's calculate the margin of error:
Margin of Error = Proportion × Z-value × √(1 - Proportion) / √Sample Size
Margin of Error = 0.68 × 1.96 × √(1 - 0.68) / √1008
Margin of Error ≈ 0.68 × 1.96 × 0.47 / 31.78
Margin of Error ≈ 0.032
Finally, we can find the upper and lower estimates by adding and subtracting the margin of error from the estimated number:
Upper Estimate = Estimated Number + Margin of Error
Upper Estimate ≈ 19.04 million + 0.032 million
Upper Estimate ≈ 19.072 million
Lower Estimate = Estimated Number - Margin of Error
Lower Estimate ≈ 19.04 million - 0.032 million
Lower Estimate ≈ 19.008 million
Therefore, the upper estimate for the number of Canadian adults who agree the penny should be taken out of circulation is approximately 19.072 million, and the lower estimate is approximately 19.008 million.