In a certain city, there are 10,000 persons age 18 to 24. A simple random sample of

500 such persons is drawn, of whom 200 turn out to be currently enrolled in college. Find a 90%
con¯dence interval for the percentage of persons age 18 to 24 in the city who are attending college.

Try using a binomial proportion CI formula:

CI90 = p + or - 1.645(√pq/n)
...where p = proportion in the problem, q = 1 - p, n = sample size, √ = square root, and + or - 1.645 represents 90% CI using a z-table.

Your data:
p = 200/500
q = 1 - p
n = 500

Convert all fractions to decimals. Substitute values into the formula and determine the confidence interval.

I hope this will help get you started.

500.12

To find a 90% confidence interval for the percentage of persons age 18 to 24 in the city who are attending college, you can use the following formula:

Confidence Interval = Sample Proportion ± Margin of Error

To calculate the sample proportion, divide the number of individuals in the sample who are currently enrolled in college (200) by the sample size (500):

Sample Proportion = (Number of individuals currently enrolled in college) / (Sample size)

Sample Proportion = 200 / 500 = 0.4

The margin of error depends on the sample size and the desired confidence level. For a 90% confidence level, you need to find the critical value of the standard normal distribution (Z*) that corresponds to a confidence level of 90%. This value can be obtained from a standard normal distribution table or calculated using statistical software.

Assuming a Z* value of 1.645 for a 90% confidence level, the margin of error is calculated as:

Margin of Error = Z* * √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]

Margin of Error = 1.645 * √[(0.4 * 0.6) / 500]

Margin of Error ≈ 0.0343

Now, we can calculate the confidence interval by adding and subtracting the margin of error from the sample proportion:

Confidence Interval = 0.4 ± 0.0343

Confidence Interval = (0.3657, 0.4343)

Therefore, the 90% confidence interval for the percentage of persons age 18 to 24 in the city who are attending college is approximately 36.57% to 43.43%.