Question

A random sample of ni = 219 people who live in a city were selected and 72 identified as a "dog person." A random sample of n2 = 104 people who live in a rural area were selected and 58 identified as a "dog person." Find the 97% confidence interval for the difference in the proportion of people that live in a rural area who identify as a "dog person" and the proportion of people that live in a city who identify as a "dog person." 1. State the value of the sample proportion for those who live in the city. Round to 2 decimals. 2. State the value of the sample proportion for those who live in a rural area. Round to 2 decimals. 3. Is nip > 5? (yes or no) 4. Is ni(1-P) > 5? (yes or no) 5. Is n2p2 > 5? (yes or no) 6. Is n2(1 - P2) > 5? (yes or no) 7. Find the value of the standard error. Round to 3 decimals. 8. Find the value of z needed to create the confidence interval. Round to 2 decimals. 9. Find the confidence interval. Round your final answers to 3 decimals. In your calculations, use your values from earlier. < Select an answer <

Answer 1

1)

p1 = 72/219 = 0.33

2)

p2 = 58/104 = 0.56

3)

yes
4)

yes

5)

yes

6)

yes

7)

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.33 * (1-0.33)/219 + 0.56*(1-0.56)/104)
SE = 0.058

8)

For 0.97 CI, z-value = 2.17

9)

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.33 - 0.56 - 2.17*0.058, 0.33 - 0.56 + 2.17*0.058)
CI = (-0.356 , -0.104)

-0.356 < pc - pr < -0.104