A study was done on comparing the average earnings for college graduates from Io
ID: 3396804 • Letter: A
Question
A study was done on comparing the average earnings for college graduates from Iowa compared to the average earnings of college graduates from Illinois. Based on the results below, can it be concluded that there is a difference in the mean earnings for Iowa and Illinois graduates at a .05 level of significance?
Iowa
Illinois
Sample Mean
$42187
$48792
Population Standard Deviation
$7913
$9812
Sample Size
40
40
Iowa
Illinois
Sample Mean
$42187
$48792
Population Standard Deviation
$7913
$9812
Sample Size
40
40
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 42187
X2 = 48792
Calculating the standard deviations of each group,
s1 = 7913
s2 = 9812
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 40
n2 = sample size of group 2 = 40
Also, sD = 1993.056152
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = -3.314005977
where uD = hypothesized difference = 0
Now, the critical value for z is
zcrit = +/- 1.96
As |z| > 1.96, WE REJECT THE NULL HYPOTHESIS.
Thus, there is a significant difference in the mean earnings for Iowa and Illinois graduates at a .05 level of significance. [CONCLUSION]
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