In a recent survey teenagers were asked to indicate how many

In a recent survey, teenagers were asked to indicate how many 20-ounce bottles of sports drinks they consume in a typical week. The descriptive statistics revealed that males consumed 9 bottles on average and that females consumed 7.5 bottles of sport drinks on average. The respective SDs were 4 and 4. Both samples were of size 30. Construct the 80% confidence interval for the difference between the number of bottles consumed by male teens and that by female teens.

Solution

Given a=1-0.80=0.2, Z(0.1) =1.28 (from standard normal table)

So the lower bound is

(xbar1-xbar2) - Z*sqrt(s1^2/n1+s2^2/n2)

=(9-7.5)-1.28*sqrt(4^2/30+4^2/30)

=0.1780217

So the upper bound is

(xbar1-xbar2) + Z*sqrt(s1^2/n1+s2^2/n2)

=(9-7.5)+1.28*sqrt(4^2/30+4^2/30)

=2.821978