Confidence Limits for Proportion in CFA Level 1 Exam

Explanation

Interval estimate can be found from p +/- z[p(1-p)/n]^0.5. Here we have n = 500, p = 350/500 = 0.7 and z = 2.58 (for 99%). Therefore 0.7 +/- 2.58*0.02049 and we get 0.647 and 0.7529.

To determine the confidence limits for the proportion of voters who plan to vote for the Democratic incumbent, we can use the formula for confidence intervals for proportions.

The formula is:

p̂ ± Z * √[(p̂ * (1 - p̂)) / n]

Where: p̂ is the sample proportion (350/500 = 0.7) Z is the z-score corresponding to the desired confidence level (0.99) n is the sample size (500)

First, we need to find the z-score corresponding to the 0.99 confidence level. The z-score represents the number of standard deviations from the mean. We can use a standard normal distribution table or a calculator to find the z-score.

The z-score for a 0.99 confidence level is approximately 2.33.

Now, we can substitute the values into the formula:

0.7 ± 2.33 * √[(0.7 * (1 - 0.7)) / 500]

Calculating the expression within the square root:

0.7 ± 2.33 * √[(0.7 * 0.3) / 500] 0.7 ± 2.33 * √[0.21 / 500] 0.7 ± 2.33 * √[0.00042]

Simplifying:

0.7 ± 2.33 * 0.0205 0.7 ± 0.0476

Therefore, the confidence limits for the proportion of voters who plan to vote for the Democratic incumbent are:

Lower limit = 0.7 - 0.0476 = 0.6524 (approximately 0.652) Upper limit = 0.7 + 0.0476 = 0.7476 (approximately 0.748)

So, the correct answer is not provided in the options given.