Question

Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 246 with 64% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

Answer 1

To find the 90% confidence interval, we use the formula (p' - EBP, p' + EBP) where p' is the sample proportion and EBP represents the margin of error. Substituting the given values, the 90% confidence interval for the sample with 64% successes and a size of 246 is (0.606, 0.674).

Step-by-step explanation:

To calculate the 90% confidence interval for a sample of size 246 with 64% successes, we can use the formula:

(p' - EBP, p' + EBP)

Plug in the values:

p' = 0.64

EBP = margin of error = (z-value) * (standard error) = 1.645 * sqrt((p' * (1-p')) / n)

where z-value is the z-score corresponding to the confidence level (90% in this case), and n is the sample size.

Calculating the margin of error and substituting in the values:

EBP = 1.645 * sqrt((0.64 * (1-0.64)) / 246) = 0.034
Thus, the 90% confidence interval is (0.64 - 0.034, 0.64 + 0.034) = (0.606, 0.674).