In: Statistics and Probability
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 =
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