Question

Assume that a sample is used to estimate a population proportion p. find the 95% confidence interval for a sample of size 393 with 37% successes. enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

Answer 1

To calculate the 95% confidence interval for a sample proportion, use the formula (p' - EBP, p' + EBP), where p' is the sample proportion and EBP is the error bound of proportion. Substitute the values and calculate the error bound to find the confidence interval.

Step-by-step explanation:

To calculate the 95% confidence interval for a sample proportion, we can use the formula:

(p' - EBP, p' + EBP)

where p' is the sample proportion and EBP is the error bound of proportion.

In this case, the sample size is 393 and the proportion of successes is 37%. So, p' = 0.37. We can calculate the error bound (EBP) using the formula:

EBP = Z * sqrt((p' * q') / n)

Where Z is the appropriate z-value for a 95% confidence interval, which is approximately 1.96. And q' = 1 - p' = 1 - 0.37 = 0.63.

Substituting the values, we get:

EBP = 1.96 * sqrt((0.37 * 0.63) / 393) ≈ 0.0435

Therefore, the 95% confidence interval is:

(0.37 - 0.0435, 0.37 + 0.0435) = (0.3265, 0.4135)