Question

Is there a difference in the proportion of construction workers who are under 35 years of age and the proportion of telephone repair people who are under 35 years of age? Suppose a study is conducted in Calgary, Alberta, using random samples of 337 construction workers and 287 telephone repair people. The sample of construction workers includes 300 people under 35 years of age and the sample of telephone repair people includes 196 people under that age. Use these data to construct a 90% confidence interval to estimate the difference in proportions of people under 35 years of age among construction workers and telephone repair people.

Appendix A Statistical Tables

(Round the intermediate values to 3 decimal places. Round your answers to 3 decimal places.)


  ≤ p₁ − p₂ ≤   

Answer 1

Given that,

For sample 1 : n1 = 337, x1 = 287 and

P1 = 287/337 = 0.8516

For sample 2 : n2 = 300, x2 = 916 and

P2 = 196/300 = 0.6533

A 90% confidence level has significance level of 0.10 and critical value is,

Za/2 = 1.645

Margin of error (E) is,

E = 1.645 * 0.8516* (1 – 0.8516) 337 0.6533 * (1 – 0.6533) = 0.0553 300

The 90% confidence interval to estimate the difference in proportions of people under 35 years of age among construction workers and telephone repair people is,

(p1 - P2) - E p1 - p2 < (01 - p2) + E

(0.8516 - 0.6533) -0.0553 ≤ p1 - p2 ≤ (0.8516 - 0.6533) + 0.0553

0.1983 - 0.0553 ≤ p1 - p2 ≤ 0.1983 + 0.0553

0.1430 ≤ p1 - p2 ≤ 0.2536

Answer : 0.143 ≤ p1- p2 ≤ 0.254