A 2014 Gallup Poll of 1028 adults found that 216 thought abortion should be illegal in all circumstances, a decrease of 2 percentage points from the record high in 2009. We are 95% confident that between ___% and ___% of all adults thought abortion should be illegal in all circumstances.
19
To find the range between which we can be 95% confident that the percentage of adults who thought abortion should be illegal in all circumstances falls, we need to calculate the margin of error and then subtract and add it to the observed percentage.
First, let’s calculate the margin of error using the formula:
Margin of Error = Z * (√(p * (1-p))/n)
Where:
Z is the number of standard deviations corresponding to the desired confidence level (for 95% confidence, Z = 1.96),
p is the observed proportion (216/1028 = 0.2101),
and n is the sample size (1028).
Now let's plug in the values into the formula:
Margin of Error = 1.96 * (√(0.2101 * (1-0.2101))/1028)
After evaluating this equation, the margin of error is approximately 0.0191 or 1.91%.
To find the range, we subtract and add the margin of error to the observed percentage:
Lower Range = 21.01% - 1.91% = 19.10%
Upper Range = 21.01% + 1.91% = 22.92%
Therefore, we can be 95% confident that between 19.10% and 22.92% of all adults thought abortion should be illegal in all circumstances.