The upper limit of the 85% confidence interval for the population proportion p, given that n = 60 and = 0.20, is 0.274.

Question

The upper limit of the 85% confidence interval for the population proportion p, given that n = 60 and  = 0.20, is 0.274.

Quizplus · Accepted Answer

Since the upper limit of the 85% confidence interval is 0.274, we know that the margin of error is 0.274 - 0.20 = 0.074. Using the formula for the margin of error, we can calculate the standard error:

margin of error = z*(standard error)

where z is the z-score corresponding to the confidence level (in this case, z=1.44 for 85% confidence) and the standard error is given by:

standard error = sqrt(p*(1-p)/n)

Plugging in the values we know, we can solve for p:

0.074 = 1.44*sqrt(p*(1-p)/60)

0.051 = sqrt(p*(1-p)/60)

0.051^2 = p*(1-p)/60

0.003 = p*(1-p)

This is a quadratic equation that can be solved using the quadratic formula. The solutions are p=0.0 and p=0.998. Since the value of p must be between 0 and 1, we can reject p=0.998 as extraneous, leaving p=0.0 as the lower limit of the confidence interval. Therefore, the upper limit must be 2p=0.40, which is greater than the given value of 0.274. The statement is false.

The Upper Limit of the 85% Confidence Interval for the Population