Answer:
the 95% confidence interval is from 83.8% to 90.2%.
Explanation:
To find the margin of error and 95% confidence interval for the survey result, we need to use the following formula:
Margin of error = z * sqrt[p * (1 - p) / n]
Where:
z is the z-score for the desired confidence level. For a 95% confidence level, the z-score is 1.96.
p is the proportion of people in the sample who support stricter penalties for child abuse (87% in this case).
n is the sample size (1500 in this case).
Plugging these values into the formula, we get:
Margin of error = 1.96 * sqrt[0.87 * (1 - 0.87) / 1500] = 0.032
This means that the margin of error is approximately 3.2%.
To find the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. This gives us the following interval:
87% +/- 3.2% = 83.8% to 90.2%
So the 95% confidence interval is from 83.8% to 90.2%.