1. In a recent study, 6 students were randomly assigned to taking an in-person driving lesson and 5 were assigned to take a virtual-reality driving lesson. At the end of the class, all students took the same driving test. The research question was whether there was a difference in thenumber of errors made on the driving test for students who took the in-person versus virtual reality driving lesson? (Since the data represent number of errors, a higher number means poorer performance on the driving test.)

In-Person   Virtual Reality
M = 3           M = 4.8
SS = 4        SS = 6.8

a. What is the dependent variable in this experiment? What is the independent variable (including levels)?

b. Step 1: State the null and alternative hypothesis (symbols, not words).

c. Calculate the pooled variance

d. Explain why we use pooled variance. Stating that we need it for the standard error is not sufficient. Explain conceptually why the variation in the 2 groups is combined for the statistical test

e. Calculate the standard error.

f. Step 2: What is the t-critical and degrees of freedom for this test?

g. Step 3: Calculate the obtained t.

h. Step 4: Make a statistical decision about the null. Will you reject or retain the null based on your sample data? (Be sure to include appropriate test statistic and decision criteria).

i. Step 4 (continued): Provide a substantive conclusion about the results from your sample data. (Be sure to include the research context and descriptive statistics).

j. Calculate the effect size: r2

k. Interpret r2 in the context of this research.

l. Calculate Cohen's d for the context of this study.

m. Interpret what Cohen's d means in the context of the study.

2. From: http://www.cbsnews.com/8301-505145_162-57583333/college-grads-overconfident-in-job-prospects/
(MoneyWatch) Is this year's crop of college graduates overconfident about their job prospects?

It sure looks like it if you believe a new study conducted by consulting firm Accenture that suggests that the newest college grad are naive about the state of the labor market.

Only 15 percent of the respondents expect to earn less than $25,000, but 32 percent of grads from the previous two years are earning those modest salaries. Nearly two-thirds expect to find jobs in their field of study, yet in reality only about half of recent college grads succeeded in doing this.

Among people who graduated in 2011 and 2012, meanwhile, 41 percent said they are currently underemployed or working in jobs that do not require a college degree.

So, based on mixed results about the job market and recent graduates, a researcher is interested in differences between Freshmen and Senior college students with respect to how optimistic they are about their future (self-report 0 -10 point scale, with higher value associated with higher level of perceived optimism). For this voluntary (i.e., non-experimental) study (students were recruited at a local college campus) the researcher performed an independent samples t-test.
 
a. Based on the SPSS output below what is your conclusion? And confirm by hand the 95% confidence interval around the difference, and how it corresponds to the significance test (note: SE of difference is provided in table below).

b. Based on the output, compute the effect size r2 and in one sentence describe what it means in terms of the research question (and also if it is a small, medium, or large effect size).

c. What were the limitations with this study? What other variables might have contributed to between-year differences?