**t-test and ANOVA Exam**

A research study was conducted to explore the influence that stress might have on exam scores in a Behavioral Science statistics course. To begin the study the researchers were able to randomly select 10 participants and those participant’s stress levels were assessed using the Stress Assessment-3010 instrument. Based on the results of the assessment the students were assigned to one of two groups: Group 1 consisted of five students with negligible stress and Group 2 consisted of five students with severe stress. The next phase of the study was to have the students take the exam that consisted of 10 questions worth one point each. The following results were obtained:

Group 1:Group 2:

5 2

7 1

8 4

4 1

The researchers have hired you to analyze the data. The first issue for the researchers is they would like to know basic descriptive statistics that adequately and appropriately summarize the results on the exam. Provide the appropriate statistics along with a justification as to why you chose the statistics you did and an interpretation of each. (8 points)

The next question the researchers have is they would like to know if stress has influenced the exam results. Conduct the appropriate analysis to determine if there is a significant difference between the two groups. Follow the eight step process discussed in class. (11 points Step 1: 1, Step 2: 1, Step 3: 1, Step 4: 2, Step 5: 1, Step 6: 2, Step 7: 1, Step 8: 2)

In the next phase of the study, the researchers decided to increase the sample size to have better validity in the study. As they increased the sample size it was also determined that there were additional levels of stress found in the new participants. Based on the assessments two additional groups were discovered: “minimal stress” and “moderate stress”. The data for all groups is presented in the following table:

NegligibleMinimalModerateSevere

5 6 4 2

7 5 3 1

8 7 2 4

4 5 3 1

9 8 5 4

The researchers were interested in the new descriptive statistics for the four groups. Calculate, justify and interpret the appropriate statistics for the researchers (16 points)

The researchers are also interested in whether or not the various levels of stress have an impact on the exam scores. Analyze the data to determine if there is a significant difference between the four groups. Follow the eight-step process discussed in class. (15 points: Step 1: 1, Step 2: 1, Step 3: 1, Step 4: 4, Step 5: 1, Step 6: 4, Step 7: 1, Step 8: 2)

The final question on this take home test will be to complete the following ANOVA table by finding the 5 missing values: (5 points)

Source SS df MS Fobs

Between 1.____ 2 326.08 2.____

Within 612.75 3.____4.____

Total 5.____ 16

Based on your completed table, are the statistical results significant at an alph = .05? (2 points)

The effect size calculation for the ANOVA is called eta squared. Calculate the eta squared for this ANOVA table and interpret the results: (3 points).

Total Point Possible on the Exam: 60

Subject | Mathematics |

Due By (Pacific Time) | 04/02/2013 11:00 pm |

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