Question

5. In a random sample of 500 people in their 30's, 22% were smokers. In a random sample of 450 people in their 20's, 14% were smokers. The 95% confidence interval for the difference between the population proportions P_20's - P30's. turned out to be: -0.128 < p1 - p2 < -0.032. What does this imply?

There is not a significant difference between the smoking habits of people in their 20's and people in their 30's, but the sample showed a higher percentage of 30-somethings smoke.

Nothing can be determined from this interval.

There is not a significant difference between the smoking habits of people in their 20's and people in their 30's, but the sample showed a higher percentage of 20-somethings smoke.

A higher proportion of people in their 30's smoke than people in their 20's.

A higher proportion of people in their 20's smoke than people in their 30's.

3.2% of people in their 30's smoke while 12.8% of people in their 20's smoke.

Answer 1

The 95% confidence interval for the difference between the population proportions P20's - P30's. is -0.128 < p1 - p2 < -0.032. THis means that-

A higher proportion of people in their 30's smoke than people in their 20's.

( Because as the 95% confidence interval does not contain 0 , that means that there is a significant difference between the smoking habbits of people in their 20's and people in their 30's/\. Now since the confidence interval contains negatice numbers that means that people in their 30's smoke more than people in their 20's.)