Homework SourseA study compared the individual pretax yearly income earned
A study compared the individual pre-tax yearly income earned by residents from two states. The following table lists the statistics resulting from this study:
Calculate the upper and lower bound of the 95% confidence interval of the mean difference (State A - State B) between the income earned by individuals from the two states. Give your answers to 2 decimal places. You may find this Student\'s t distribution table useful.
a)Lower bound =
b)Upper bound =
| Yearly Income | |||
|---|---|---|---|
| Location | Sample Size | Sample Mean ($\'000s) | Sample Standard Deviation ($\'000s) |
| State A | 51 | 109 | 18 |
| State B | 63 | 75 | 33 |
Solution
The degree of freedom =n1+n2-2=51+63-2= 112
Given a=1-0.95=0.05, t(0.025,df=112) =1.98 (from student t table)
a)Lower bound = (xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)
=(109-75)-1.98*sqrt(18^2/51+33^2/63)
=24.37
b)Upper bound =(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)
=(109-75)+1.98*sqrt(18^2/51+33^2/63)
43.63
