Question

What proportion of commercial airline pilots are more than 40 years of age? Suppose a researcher has access to a list of all pilots who are members of the Commercial Airline 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 of age.

Round the answers to 3 decimal places.

Answer 1

Solution:

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

Confidence level = 85%

Critical Z value = 1.4395

(by using z-table)

Sample size = n = 89

Number of successes = x = 48

Sample proportion = P = x/n = 48/89 = 0.539325843

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.539325843 ± 1.4395* sqrt(0.539325843*(1 – 0.539325843)/89)

Confidence Interval = 0.539325843 ± 1.4395* 0.0528

Confidence Interval = 0.539325843 ± 0.0761

Lower limit = 0.539325843 - 0.0761 = 0.4633

Upper limit = 0.539325843 + 0.0761 = 0.6154

Confidence interval = (0.463, 0.615)