Find the 95% confidence interval when
P=0.90 and n=100. Round to two decimal places
To find the 95% confidence interval, we can use the formula for calculating the confidence interval for a proportion:
CI = p ± Z * √(p(1-p)/n)
where:
- p is the sample proportion (P in this case)
- Z is the critical value at 95% confidence level, which is 1.96 for a large sample size
- n is the sample size
Plugging in the values:
CI = 0.90 ± 1.96 * √(0.90 * 0.10 / 100)
CI = 0.90 ± 1.96 * √(0.09 / 100)
CI = 0.90 ± 1.96 * √(0.0009)
CI = 0.90 ± 1.96 * 0.03
CI = 0.90 ± 0.0588
Therefore, the 95% confidence interval is (0.8412, 0.9588) rounded to two decimal places.