Q. 16 - The Practice of Statistics for AP

Question

Many teens have posted profiles on sites such as Facebook and My Space. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of $170$ younger teens (ages $12$ to $14$) polled, $117$ said “Yes.” Of $317$ older teens (ages $15$ to $17$) polled, $152$ said “Yes.”$6$ A $95\%$ confidence interval for the difference in the population proportions (younger teens – older teens) is $0.120$ to $0.297$. Interpret the confidence interval and the confidence level 

Step-by-Step Solution

Answer

Interpretation confidence level: The confidence interval contains the true difference in population proportions, on average, in $95\%$ of all samples.

Step 1: Given Information

A sample survey asked random samples of teens with online profiles if they included false information in their profiles. 

Step 2: Explanation

The given $95\%$ confidence interval for the difference in population proportions is $0.120$ to $0.297$.

Interpretation: We are $95\%$ confidence that the difference in the population proportions between younger teens and older teens is between $0.120$ and $0.297$.