(I already have the answers as lower bound=11.9418 and upper bound =30.0581 I\'m

Question

(I already have the answers as lower bound=11.9418 and upper bound =30.0581 I'm just wanting to make sure this is correct before I submit it)

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 79 14 State B 66 58 34

Explanation / Answer

A confidence interval on the difference between two mean is computed using the formula

lower limit=(M1-M2)-t(SM1-M2)

Upper limit =(M1-M2)+t(SM1-M2)

now M1-M2 is the difference between the two mean=79-58=21

t or the critical value

here degree of freedom is =(51-1)+(66-1)=115

critical value for n=115 is 1.981

SM1-M2 is =sqrt(SE1 ^2+SE2^2)

SE1=14/sqrt51 =1.96     SE2 =34/sqrt66 =4.1851

SM1-M2 =sqrt(1.96^2+4.1851^2)=4.62

now the lower boundary is =21-1.981*4.62=11.84778

upper boundary is =21+1.981*4.62 =30.152

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