Homework SourseI already have the answers as lower bound119418 and upper bo
(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 |
Solution
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
