A study compared the individual pre-tax yearly income earned by residents from t
ID: 3432277 • Letter: A
Question
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 33Explanation / Answer
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.