In a random sample of 500 people aged 20-24, 22% were smokers. In a random sampl

Question

In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. A 95% confidence interval for the difference between the proportion of 20-24 year olds and the proportion of 25-29 year olds who are smokers is 0.032 < p1-p2 < 0.128.
Which of the following statements give a correct interpretation of this confidence interval?
I. We can be 95% confident that the interval 0.032 to 0.128 contains the true difference between the two population proportions.
II. There is a 95% chance that the true difference between the two population proportions lies between 0.032 and 0.128.
III. If the process were repeated many times, each time selecting random samples of 500 people aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for p1 - p2, 95% of the time the true difference between the two population proportions will lie between 0.032 and 0.128.
IV. If the process were repeated many times, each time selecting random samples of 500 people aged 20-24 and 450 people aged 25-29 and each time constructing a confidence interval for p1 - p2, 95% of the time the confidence interval limits will contain the true difference between the two population proportions.



a. II and IV

b. I and IV

c. II and III

d. I and III

Explanation / Answer

1. Use normal approximation n1p1 = 5 n2p2 = 5 n1(1-p1) = 5 n2(1-p2) = 5 but, you can just check with the smallest (450)(.14)=5.6 = 5 so we're good 2.since this is normal proportion, use z* at the 95% level, use a t-table z*=1.96 3. p1-p2 let's choose 20-24 as 1 and 25-29 as 2 0.22-0.14=0.08 4. m=z* (v((p1(1-p1)/n1)+(p2(1-p2)/n2)) m=(1.96)(v((0.22(1-0.22)/500)+(0.14(1-… m=0.0484 5. confidence interval is (p1-p2) + or - z*s (0.22-0.14) + or - (1.96)(v((0.22(1-0.22)/500)+(0.14(1-0.14… (0.0316,0.1284) or (3.16%,12.84%)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.