Question

Emilio wants to estimate the percentage of people who have a financial adviser. He surveys 350 individuals and finds that 76 have a financial adviser.

Identify the values needed to calculate a confidence interval at the 99% confidence level. Then use Excel to find the confidence interval.

Round the final answer to three decimal places.

Answer 1

he 99% confidence interval for the percentage of people who have a financial adviser is 16.5% to 26.9%.

The values needed to calculate a confidence interval at the 99% confidence level:

Sample size (n): 350

Number of successes (x): 76

Confidence level (α): 0.99

To find the confidence interval, you can use the following formula:

P ± z*√(P(1-P)/n)

where:

P: Sample proportion (x/n)

z: Z-score for the desired confidence level (2.576 for a 99% confidence level)

Using the given values, we can calculate the sample proportion (P):

P = x/n = 76/350 = 0.217

Now, we can calculate the confidence interval:

P ± z*√(P(1-P)/n)

0.217 ± 2.576*√(0.217(1-0.217)/350)

0.165 ≤ p ≤ 0.269

Therefore, the 99% confidence interval for the percentage of people who have a financial adviser is 16.5% to 26.9%.