Find the 95% confidence interval when
p=0.25 and n=94. Round to two decimal places
To find the 95% confidence interval for a proportion, we can use the formula:
CI = p ± Z * sqrt((p*(1-p))/n)
Where:
p = sample proportion
n = sample size
Z = z-score for the desired level of confidence (95% confidence level corresponds to a z-score of approximately 1.96)
Given p = 0.25 and n = 94, we can calculate the confidence interval:
CI = 0.25 ± 1.96 * sqrt((0.25*(1-0.25))/94)
CI = 0.25 ± 1.96 * sqrt(0.1875/94)
CI = 0.25 ± 1.96 * sqrt(0.00199468)
CI = 0.25 ± 1.96 * 0.04466
CI = 0.25 ± 0.0877
Therefore, the 95% confidence interval is (0.1623, 0.3377) when rounded to two decimal places.