Question
In: Statistics and Probability
Three independent random samples of community college students were obtained to find out how many hours...
Three independent random samples of community college students were obtained to find out how many hours the students spent each week doing math homework outside of the classroom. The samples were made up of students in pre-algebra, elementary algebra, and intermediate algebra.
|
PreAlg |
ElemAlg |
InterAlg |
|
1 |
5 |
9 |
|
0 |
2 |
2 |
|
1 |
3 |
3 |
|
1 |
3 |
1 |
|
2 |
2 |
4 |
|
2 |
3 |
2 |
|
2.5 |
4 |
3 |
|
3 |
2 |
5 |
|
0.5 |
4 |
7 |
|
0 |
3 |
3 |
|
1 |
3 |
4 |
|
8 |
a. How many comparisons would be required to compare the populations two at a time?
b. If we wanted an overall significance of .05 what significance would we use in each test according to the Bonferroni correction?
c. Assuming we meet the requirements, find the p-values for each of the possible two tailed tests. PreAlg and ElemAlg: p-value= PreAlg and InterAlg: p-value= ElemAlg and InterAlg: p-value= d. What is your conclusion?
Solutions
Expert Solution
- As there are total three independent random samples, therefore
to compare the populations two at a time, we need
comparisons i.e. 3. - If the desired level of significance is
and m number of hypotheses are to be tested, then according to
Bonferroni correction the significance level will be 
for each of the hypothesis under test. For the given problem,
and m=3, hence the significance level will be 0.0167 for each of
the test. - Perform two tailed t-test as the given set up holds small sample and population variance is unknown.
comparisons i.e. 3.
and m number of hypotheses are to be tested, then according to
Bonferroni correction the significance level will be 
for each of the hypothesis under test. For the given problem,
and m=3, hence the significance level will be 0.0167 for each of
the test.PreAlg and ElemAlg: p-value= 0.00026
PreAlg and InterAlg: p-value= 0.00191
ElemAlg and InterAlg: p-value=0.16060
4. Conclusion:
For each of the test, the significance level is 0.0167. The first two comparison, i.e.(i) PreAlg and ElemAlg and (ii) PreAlg and InterAlg have p-value smaller than the significance level and hence we can conclude that the hypotheses of these two comparisons are rejected at 0.0167 level of significance. Therefore students of PreAlg and ElemAlg differ significantly between themselves and the students of PreAlg and InterAlg differ significantly between themselves as well.
Again, (iii) ElemAlg and InterAlg have p-value greater than the significance level and hence we can conclude that the hypotheses of this comparisons is not rejected at 0.0167 level of significance. Therefore, there no significant difference between the students of ElemAlg and InterAlg.
orchestra answered 3 years agoRelated Solutions
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