Question

Construct a 99% confidence interval for the population proportion when the sample size is n = 540 and the sample proportion is 0.8.

Answer 1

To construct a 99% confidence interval for the population proportion, calculate the margin of error using the formula: z √((p(1-p))/n). Then, find the lower and upper bounds by subtracting and adding the margin of error to the sample proportion, respectively.

Step-by-step explanation:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Sample Proportion - Margin of Error to Sample Proportion, Sample Proportion + Margin of Error to

Sample Proportion

1. First, calculate the margin of error using the formula: z √((p(1-p))/n).
2. Next, calculate the lower bound of the confidence interval by subtracting the margin of error from the sample proportion.
3. Finally, calculate the upper bound of the confidence interval by adding the margin of error to the sample proportion.

For this question, you would calculate:

Margin of Error = z √((p(1-p))/n) = 2.58 √((0.8(1-0.8))/540) = 0.0435

Lower Bound = Sample Proportion - Margin of Error to Sample Proportion(0.8 - 0.0435 = 0.7565)

Upper Bound = Sample Proportion + Margin of Error to Sample Proportion(0.8 + 0.0435 = 0.8435)

The 99% confidence interval for the population proportion is (0.7565, 0.8435).