When a confidence interval for a population proportion is constructed for a sample size n = 100 and the value of, p = .4 the interval is based on the (Points : 1)
The mean ± standard error of the mean or SD/√n
To construct a confidence interval for a population proportion, we need to use the formula:
Confidence Interval = proportion ± margin of error
The margin of error can be calculated using the formula:
Margin of Error = z * sqrt((p * (1 - p)) / n)
Where:
- z is the z-score corresponding to the desired level of confidence
- p is the sample proportion
- n is the sample size
Now, in your case, the sample size (n) is 100, and the value of the sample proportion (p) is 0.4. However, the question does not provide the desired level of confidence or the specific z-score to use.
To calculate the confidence interval, we need to specify the desired level of confidence. Let's assume a 95% confidence level, which corresponds to a z-score of approximately 1.96. Using this information, we can calculate the margin of error:
Margin of Error = 1.96 * sqrt((0.4 * (1 - 0.4)) / 100)
Once we calculate the margin of error, we can plug it into the confidence interval formula:
Confidence Interval = 0.4 ± Margin of Error
The result will be a range of values that represents the confidence interval for the population proportion.