In a random sample of 200 registered voters, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of registered voters in the population who are Democrats.
To develop a confidence interval for the proportion of registered voters in the population who are Democrats, you can use the formula for estimating a confidence interval for a proportion.
The formula for estimating the confidence interval for a proportion is:
CI = p̂ ± (Z * √(p̂(1-p̂)/n))
where:
- CI is the confidence interval
- p̂ is the sample proportion (in this case, the proportion of Democrats in the sample)
- Z is the z-value corresponding to the desired level of confidence (e.g., for a 95% confidence level, Z = 1.96)
- n is the sample size (in this case, 200)
First, calculate the sample proportion of Democrats:
p̂ = 120/200
p̂ = 0.6
Next, calculate the margin of error:
Margin of Error = Z * √(p̂(1-p̂)/n)
Margin of Error = 1.96 * √(0.6 * (1-0.6)/200)
Margin of Error = 0.060
Finally, calculate the confidence interval:
CI = p̂ ± Margin of Error
CI = 0.6 ± 0.060
Therefore, the 95% confidence interval for the proportion of registered voters in the population who are Democrats is (0.54, 0.66).