statistics help II

Name:

Answer the questions below to the best of your ability. Partial credit will be awarded where possible. You MUST SHOW YOUR WORK for full credit for calculation problems.

Completion (12 points)

Complete each sentence or statement.

1. A Type _____ error is committed when one rejects the null hypothesis when it is true, whereas a Type _____ error is committed when one retains the null hypothesis when it is false (2 points).

2. If my test statistic is more extreme than my critical value then I would ______________ the null hypothesis; if my test statistic was not more extreme than my critical value then I would _______________________ the null hypothesis (2 points).

3. I use a t distribution instead of a z distribution as my test distribution when I don’t know ________ (1 point).

4. I want to see if eating chocolate cake makes people increase their exam scores. This is an example of a ________ - tailed test (1 point).

5. A t distribution looks like a _______ distribution, except that the t distribution is flatter (1 point).

6. Whereas a null hypothesis significance test tells us if there is or is not a significant difference, the _______________________ tells us how important a difference is (1 point).

7. If you have a TOTAL of 10 people, the degrees of freedom for an independent design would be ______________________; however if you have a dependent design the degrees of freedom would be _________________________ (2 points).

8. How tall/flat a t distribution is depends upon ________________________ (1 point).

9. Our p-value reflects how probable our data is, assuming that the _____________________ hypothesis is true (1 point).

Short Answer (9 points)

1. Define what power is and name two things (we talked about three in class) that will increase power in an experiment. For each of the factors you name that influences power, describe how it influences power (i.e. does increasing that factor increase power or decrease power?) (5 points). Extra credit: Name the third factor that influences power, and how it influences it (i.e. does increasing that factor increase power or decrease power?) (1 point each).

2. Name one major advantage of using a repeated-measures design (related-samples t test) over an independent-samples design, and name at least one major disadvantage or problem that arises by using repeated-measures (2 points). Make sure you label which is the advantage, and which is the disadvantage.

3. For an independent measures design, we need to make an assumption about our independent groups for our independent samples t test to be valid. This is called the homogeneity of variance assumption. Define what this assumption is and list the statistical test we use to assess it (2 points).

Problems (31 points)

Remember you MUST show your work to receive full credit.

1. The SAT has a mean of 500 and a standard deviation of 110. Let us assume that the distribution of SAT scores is approximately normal.

a. For a sample of n = 25, what is the probability of getting a sample mean of 480 or lower (3 points)?

b. For a sample of n = 100, what is the probability of getting a sample mean between 500 and 540 (3 points)?

2. Dr. Bliss is comparing the effectiveness of two video game-based training modules. He wants to see which module yields better training. He randomly assigned soldiers to two different training modules. Once their training is complete, he tests their performance using a battle simulator. Higher numbers indicate better performance. Training Group A has M = 10, n = 11, and SS = 900; Training Group B has M = 18, n =9, and SS = 750.

a. What is the alternative hypothesis in both words and statistical notation / symbols? (2 points)

b. What is the null hypothesis in both words and statistical notation / symbols? (2 points)

c. What is the critical t value? (1 point)

d. Compute the test statistic. (4 points)

e. Do you retain or reject the null? What do you conclude from the data? (2 points)

3. Numerous studies have shown that IQ scores have been increasing, generation by generation. To demonstrate this phenomenon, a researcher obtains an IQ test that was written in 1970. At the time the test was prepared, it was standardized to produce a population mean of μ = 100. The researcher administered the test to a random sample of n = 25 high school students and gets a sample mean of M = 121 with SS = 6000. We only want to test if IQ scores ARE INCREASING significantly over time. Use alpha = .01.

f. What is the alternative hypothesis in words and statistical terms / notation? (2 points)

g. What is the null hypothesis in words and in statistical terms / notation? (2 points)

h. What is the critical value? (1 point)

i. Compute the test statistic. (4 points)

j. Do you retain or reject the null? What do you conclude regarding the data? (2 points)

k. Compute and interpret an effect size. You’ve learned two effect size measures in class, but you only need to compute one: your choice. (3 points)

4. For an independent-samples design, Group A has M = 88 and SS = 1240, Group B has M = 67 and SS = 1920. Both groups have n = 16 participants. Using an alpha = .05, test the homogeneity of variance assumption. What do you conclude? (4 points)

5. For a repeated-samples design, the mean difference score is MD = 14.3, and the variance for the difference scores is 144. For n = 16, compute the appropriate test statistic. Also compute a measure of effect size. (4 points)

Research Scenarios (9 points)

1. Last fall, a sample of n=64 freshmen were selected to participate in a new course designed to improve social responsibility (e.g. community service, recycling, keeping up with current events, etc.). To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshman were given a survey asking about the kind of behaviors that they engage in that reflect social responsibility (e.g. volunteering at soup kitchens, reading the newspaper, picking up trash, etc.). The social responsibility mean for the entire freshman class was μ = 74. (3 points)

a. What is the independent variable or predictor?

b. What is the dependent variable or criterion?

c. What type of statistical test would you use?

2. Dr. Dunaway conducted a series of experiments examining the effects of font on memory. She collected a series of statements and then modified each statement to make each one a different font. The Times New Roman sentences were then presented to one group of participants and the sentences of varying fonts were presented to another group. Each group was then given a test to determine how many sentences they could remember. (3 points)

a. What is the independent variable or predictor?

b. What is the dependent variable or criterion?

c. What type of statistical test would you use?

3. A psychologist is testing a new drug to characterize its ability to prevent headaches. The headache threshold is measured for a sample of n = 16 participants by determining how long they can listen to Kenny G before a headache develops. After the initial baseline is established, each participant receives the drug, and then the headache threshold is measured once again using the musical stylings of Kenny G. (3 points)

a. What is the independent variable or predictor?

b. What is the dependent variable or criterion?

c. What type of statistical test would you use?

SPSS (5 points)

Use SPSS to answer the questions below.

Enter the following scores into SPSS, naming them StatsStart and StatsEnd.

StatsStart	StatsEnd
2	2
6	6
3	6
6	7
6	4
2	5
2	5
1	6
4	4
7	4

These scores represent the values from students who were asked how much they like statistics. Each student answered this question once at the start of the semester, and once at the end of the semester. They could respond on a scale of 1 (I hate statistics) to 7 (I love statistics). The values above reflect the answers for the same 10 students at the start of the semester and the end of the semester.

1. Use SPSS to calculate the repeated-measures t test for these data. Right-click to copy the associated tables from your SPSS output, and paste them into Word here. Include both the descriptives table (with M and SD) and the test results table (with t, df, etc.) (2 points):

2. Write a statement that presents your results in APA format, similar to your APA formatted write-up for Lab 5 (chapter 13’s statement). (3 points)