stats help
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Part I. Multiple choice (2 point each, 10 points total)
1. Which of the following is an assumption of ANOVAs?
a. Homogeneity of means
b. Homogeneity of variance
c. Heterogeneity of variance
d. Heterogeneity of means
e. None of the above is an assumption of ANOVAs
2. Which of the following is (are) a characteristic(s) of the F distribution?
a. It is normally distributed
b. There is just one distribution
c. It is positively skewed
d. It is negatively skewed
e. b and c
3. Which of the following is an advantage of using confidence intervals instead of a null-hypothesis approach?
a. Reduces our Type I error rate
b. Enables us to compare more than two groups at a time
c. Allows us to determine the significance of effect of the independent variable
d. Gives us information on the size of the effect
e. Increases our statistical power
4. You are conducting an independent samples t test. If you construct a 95% confidence interval and it contains zero, what should you conclude?
a. We can be 95% confident that μ1 ≠ μ2; We can reject the null hypothesis
b. We cannot be 95% confident that μ1 = μ2; We cannot reject the null hypothesis
c. We cannot be 95% confident that μ1 ≠ μ2; We cannot reject the null hypothesis
d. We can be 95% confident that μ1 = μ2; We can reject the null hypothesis
e. We can be 95% confident that μ1 = μ2; We can reject the null hypothesis
5. In the store of The Boy Who Cried Wolf, the little boy made a ___________ error because he called for help when no wolf was shown. The villagers did not believe him anymore and did not help the little boy when he called for help again and there was a wolf coming. The villagers made a _________ error.
a. Type 1; Type 2
b. Type 2; Type 1
c. Type 1; Type 1
d. Type 2; Type 2
e. None of the above is correct
Part II. Application Questions. Be sure to answer all parts of a question and show ALL OF YOUR WORK, to receive full or partial credit. Round to 2 decimal points for the final calculation outcomes.
6. (15 points) A university is considering implementing one of the following three grading systems: 1) all grades are pass–fail, 2) 90% of the grades are on the 4.0 system and 10% are pass–fail, and 3) all grades are on the 4.0 system. A survey is taken to determine whether grading system preference depends on undergraduate major. A random sample of 500 students from three majors were asked which of the grading systems they prefer.
What test should you use? How do you know?
State the H1 and H0.
Calculate the appropriate statistic. Use the table to help organize your calculations
|
|
Pass-Fail |
4.0 & Pass-fail |
4.0 |
|
|
Fine Arts |
26 |
55 |
19 |
|
|
Arts and Sciences |
24 |
118 |
58 |
|
|
Engineering |
20 |
112 |
68 |
|
|
|
|
|
|
|
|
|
|
|
|
.
d. Make a decision (α = .05).
e. Draw a conclusion.
7. (30 points) A researcher explores whether certain types of early experiences influence infants’ happiness. There are 3 interventions. Parents are given either: (1) an infant carrier to encourage babywearing, (2) books to read to their baby, (3) songs to sing with their baby. After using the infant products, parents completed a survey of their infant’s happiness. Higher scores indicate higher happiness levels.
|
Baby carrier |
Baby books |
Baby songs |
|
2 |
6 |
10 |
|
6 |
9 |
10 |
|
7 |
7 |
2 |
|
6 |
10 |
2 |
|
1 |
4 |
3 |
|
7 |
9 |
9 |
|
2 |
8 |
6 |
|
3 |
10 |
8 |
|
4 |
10 |
9 |
a. Fill in the missing values in the following table.
|
Source |
SS |
df |
s2 |
Fobt |
|
Between Groups |
|
|
|
|
|
Within Groups |
|
|
|
|
|
Total |
239.63 |
|
|
b. What is your statistical decision and conclusion? Use
|
Pre-Meditation |
Post-Meditation |
|
1 |
3 |
|
5 |
7 |
|
3 |
6 |
|
4 |
6 |
|
5 |
5 |
|
2 |
4 |
|
3 |
6 |
8. (30 points) The following table compared 7 students’ moods before and after participating in a 20-minute meditation. Students reported their moods on a scale from 1 (very bad) to 7 (very good). Use the following data to determine whether the meditation successfully improved students’ moods, α = 0.05.
a. What is your null and alternative hypotheses?
b. Calculate the appropriate statistic.
c. What is your conclusion?
d. Calculate Cohen’s d and interpret it.
9. (20 points) You investigated the effect of a stress management intervention on preschoolers with anxiety disorders. 25 kids received the stress management intervention; 37 kids received no intervention. One month after the intervention, the kids reported their average stress level in a month. The mean stress level in the intervention group is 5, with sums of squares (SS) of 6. The mean stress level in the no intervention group is 7, with sums of squares (SS) of 9. What is your conclusion? Use
10. (5 extra credits) Describe a research question and the research design (different from the questions in the exam) that you are interested in. What is the appropriate statistical test for your research?