P(proportion) is 0.05446, n is 863 and a 90% confidence interval is required. What is this confidence interval?
To find the confidence interval, we can use the formula:
Confidence Interval = P ± Z * sqrt((P * (1-P)) / n)
Where:
P = Proportion (0.05446 in this case)
Z = Z-value for the desired confidence level (90% confidence level corresponds to a Z-value of 1.645)
n = Sample size (863 in this case)
Plugging in the values:
Confidence Interval = 0.05446 ± 1.645 * sqrt((0.05446 * (1-0.05446)) / 863)
Now, let's calculate the confidence interval:
Confidence Interval = 0.05446 ± 1.645 * sqrt((0.05446 * 0.94554) / 863)
Confidence Interval = 0.05446 ± 1.645 * sqrt(0.05137 / 863)
Confidence Interval = 0.05446 ± 1.645 * 0.00609
Confidence Interval = 0.05446 ± 0.01003
Now we can calculate the lower and upper bounds of the confidence interval:
Lower bound = 0.05446 - 0.01003 = 0.04443
Upper bound = 0.05446 + 0.01003 = 0.06449
Therefore, the 90% confidence interval is (0.04443, 0.06449).