Are medical students more motivated than law students?A randomly selected group of each were administered a survey ofattitudes toward Life, which measures motivation for upwardmobility. The scores are summarized below. The researchers suggestthat there are occupational differences in mean testosterone level.Medical doctors and university professors are two of theoccupational groups for which means and standard deviations arerecorded and listed in the following table.
| Group | Sample size | Mean | StDev |
|---|
| Medical | n1=4n1=4 | x¯1=87.01x¯1=87.01 | s1=6.7s1=6.7 |
|---|
| Law | n2=10n2=10 | x¯2=85.95x¯2=85.95 | s2=16.5s2=16.5 |
|---|
Let us denote:
- μ1:μ1: population mean testosterone among medical doctors,
- μ2:μ2: population mean testosterone among universityprofessors,
- σ1:σ1: population standard deviation of testosterone amongmedical doctors,
- σ2:σ2: population standard deviation of testosterone amonguniversity professors.
If the researcher is interested to know whether the meantestosterone level among medical doctors is higher than that amonguniversity professors, what are the appropriate hypotheses heshould test?
H0:μ1=μ2H0:μ1=μ2  against  Ha:μ1≠μ2Ha:μ1≠μ2.
H0:x¯1=x¯2H0:x¯1=x¯2  against  Ha:x¯1>x¯2Ha:x¯1>x¯2.
H0:x¯1=x¯2H0:x¯1=x¯2  against  Ha:x¯1H0:μ1=μ2H0:μ1=μ2  against  Ha:μ1>μ2Ha:μ1>μ2.
H0:x¯1=x¯2H0:x¯1=x¯2  against  Ha:x¯1≠x¯2Ha:x¯1≠x¯2.
H0:μ1=μ2H0:μ1=μ2  against  Ha:μ1<μ2Ha:μ1<μ2.
Case 1: Assume that the population standard deviationsare unequal, i.e. σ1≠σ2σ1≠σ2.
What is the standard error of the difference in sample meanx¯1−x¯2x¯1−x¯2? i.e. s.e.(x¯1−x¯2)=s.e.(x¯1−x¯2)= [answer to 4decimal places]
Rejection region: We reject H0H0 at 1% level of significanceif:
t<−3.05t<−3.05.
t>3.05t>3.05.
t<−2.68t<−2.68.
t>2.68t>2.68.
|t|>3.05|t|>3.05.
None of the above.
The value of the test-statistic is: Answer to 3 decimalplaces.
If α=0.01α=0.01, and the p-value is 0.4335, what will be yourconclusion?
There is not enough information to conclude.
Do not reject H0H0.
Reject H0H0.
Case 2: Now assume that the population standarddeviations are equal, i.e. σ1=σ2σ1=σ2.
Compute the pooled standard deviation, spooledspooled [answerto 4 decimal places]
Rejection region: We reject H0H0 at 1% level of significanceif:
t>3.05t>3.05.
t<−2.68t<−2.68.
t>2.68t>2.68.
|t|>3.05|t|>3.05.
t<−3.05t<−3.05.
None of the above.
The value of the test-statistic is: Answer to 3 decimalplaces.
If α=0.01α=0.01, , and the p-value is 0.4525, what will be yourconclusion?
Reject H0H0.
Do not reject H0H0.
There is not enough information to conclude.
