In a survey of 1000 registered U.S. voters, 55% respond that they support health care reform. What is the 95% confidence interval for the true percentage of U.S. registered voters who support health care reform?
50%-60%
55%-60%
51%-59%
52%-58%
49%-47%
52%-58%
To calculate the 95% confidence interval for the true percentage of U.S. registered voters who support health care reform, you can use the following formula:
Confidence interval = sample proportion ± margin of error
The margin of error can be calculated using the formula:
Margin of error = z *√(p(1-p)/n)
Where:
- z is the z-score corresponding to the desired confidence level (for a 95% confidence level, the z-score is approximately 1.96).
- p is the sample proportion (in this case, it is 55% which can be expressed as 0.55).
- n is the sample size (in this case, it is 1000).
Now, let's plug in these values into the formulas:
Margin of error = 1.96 *√(0.55(1-0.55)/1000)
Calculating this, the margin of error is approximately 0.023.
Now, we can calculate the confidence interval:
Confidence interval = 0.55 ± 0.023
Calculating this, the confidence interval is approximately 0.527 to 0.573.
Therefore, the correct answer is: 52%-58%