Question

what proportion of commercial airline pilots are more than 40 years of age? suppose an analyst has access to a list of all pilots who are members of the air line pilots association. if this list is used as a frame for the study, she can randomly select a sample of pilots, contact them, and ascertain their ages. from 89 of these pilots so selected, she learns that 48 are more than 40 years of age. construct an 85% confidence interval to estimate the population proportion of commercial airline pilots who are more than 40 years

Answer 1

To construct an 85% confidence interval to estimate the proportion of commercial airline pilots who are over 40 years old, use the formula p' +/- z * standard error, where p' is the sample proportion and z is the z-score for the desired confidence level. In this case, the confidence interval is (0.468, 0.610).

Step-by-step explanation:

To construct an 85% confidence interval to estimate the population proportion of commercial airline pilots who are more than 40 years old, we can use the sample data. From the information given, we have a sample size of 89 pilots and 48 of them are more than 40 years old.

First, we calculate the sample proportion, which is the number of pilots more than 40 years old divided by the total sample size:

Sample proportion (p') = 48/89 = 0.5393

Next, we calculate the standard error, which is the square root of (p'(1-p')/n), where n is the sample size:

Standard error = sqrt((0.5393(1-0.5393))/89) = 0.0531

Now we can construct the confidence interval using the formula:

Confidence interval = p' +/- z * standard error

Where z is the z-score corresponding to the desired confidence level. For an 85% confidence level, z = 1.440

Confidence interval = 0.5393 +/- 1.440 * 0.0531

Confidence interval = (0.468, 0.610)