A subsample of the 2006 MTF survey suggests that adolescents are generally concerned with social issues. In fact, 70% of the 1,482 respondents who answered the question reported that they either sometimes or often think about social issues. Estimate 95% and 99% confidence intervals the percentage of all adolescents who sometimes or often think about social issues. Please round to a whole number.

a) (68%,72%)    

b) (67%,73%)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1482

Proportion of reported that they either sometimes or often think about social issues =

a) 95% Confidence interval:

Putting the values, we get:

b) 99% Confidence interval:

Putting the values, we get:

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.