posted by TLC .
Use the following information and data for questions 1-5. A group of researchers hypothesizes that listening to music while studying for an exam influences test scores. They randomly selected 28 subjects and randomly assigned them to one of four groups. All groups studied for a test one hour a day for a week. Group 1 studied without music. Group 2 studied with classical music in the background, group 3 with country, and group 4 with jazz. The following are the final test scores:
Group 1 Group 2 Group 3 Group 4
50 59 60 49
45 57 49 45
42 57 56 45
41 55 55 42
40 56 54 41
39 53 51 39
44 48 46 47
What test is most appropriate for this data and hypothesis?
Analysis of Variance
What is the null hypothesis?
mGroup1 > mGroup 2 > mGroup3 > mGroup4
mGroup1 < (mGroup 2 + mGroup3 + mGroup4) / 3
mGroup1 = mGroup 2 = mGroup3 = mGroup4
What is the value for the observed test statistic?
The degrees of freedom for the test are:
3 and 6
4 and 27
3 and 24
4 and 28
If the alpha level chosen is .01, the researchers can conclude from the F-test results that:
Groups 1 and 2 are significantly different from Groups 3 and 4
Groups 2, 3, and 4 are significantly different than the Control (Group 1).
There is a significant difference among these groups.
There are no significant differences among the groups.
Here are a few comments to get you started.
There is a hint of the type of test to perform on this data in Question 5. (Hint: F-test)
Null hypothesis uses equal signs.
Compute the test statistic based on the test chosen for the data.
Degrees of freedom for this type of F-test:
To calculate df between:
k - 1
Note: k = number of levels or groups.
To calculate df within:
N - k
Note: N = total number of values in all levels or groups.
If the null is rejected, there is a significant difference among the groups.
If the null is not rejected, then there is no difference.
I'll let you take it from here.