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:

Yearly Income
Location	Sample Size	Sample Mean ($'000s)	Sample Standard Deviation ($'000s)
State A	51	86	19
State B	61	74	26

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.

a)Lower bound =

b)Upper bound =

Answer 1

SOLUTION:

From given data,

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:

Let us consider ,

n₁ = 51 ;  n₂ = 61

= 86 ;   = 74

= 19 ;   = 26

Significance level = = 0.05

Critical value = t* =  1.982

Margin of error =

=

=

=

(a) Lower limit =

= ( 86 - 74) -

= 12- 8.446296

=  3.553704

(b)Upper limit =

= ( 86 - 74) +

= 12+ 8.446296

=  20.446296