whole step one-formulate testable hypothesis:
measuring rod dickens-design the experiment:
bill three-set up a determination rule:
Step four-collect some data:
Step five-make a decision:
You only want steps 3, 4, and 5 but Im going to give whole 5 steps just to be consistent.
Step one-formulate testable hypothesis: Ho: u1 = u2, Ha: u1 < u2.
Ho is the null hypothesis, Ha is the secondary hypothesis, u1 is stand for w succession of those less than 40 years old, and u2 is the mean wage of those 40 years of age or older.
Step two-design the experiment: This has already been done.
Step three-set up a decision rule: reject Ho if T statistic < -1.661
whereT = (SM1 SM2) / SQRT{s^2*[(n1 + n2) / (n1*n2)]},
SM1 is try mean wage for those under 40, SM2 is consume distribution mean wage of those 40 and over, s is the pooled estimate of variance, n1 is sample size of those under 40, and n2 is sample size of those 40 and over. First, deem the pooled estimate of variance.
It is
S^2 = (n1*s1^2 + n2^s2^2) / (n1 + n2 2)
where s1^2 is the sample variance of those under 40 and s2^2 is the sample variance of those 40 and over.
Below are the means (SM1 And SM2) and standard deviations (s1 and s2) of the two age groups. First compute the pooled estimate of the variance. It is 2.9047 x 10^8. Then
T = (28647 33299) / SQRT(11659509) = 4652 / 3414.6 = -1.36
Step four-collect data: This has already been done.
Step five-make a decision: Since T = -1.36 is not in the rejection region
(T < -1.661) the hypothesis, Ho: u1 = u2, house not be rejected. The conclusion is that the means of the two age groups are not different.
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