We've pretty much reviewed now all of the analysis methods we've learned in this course, as well as when it would be appropriate to use each analysis method. In summary:
 First, ask what type of response has been measured. Do we summarize it by a proportion or a mean (median)?
 Then, ask how many groups are being studied and/or compared.
 Then, decide whether we should conduct a hypothesis test or calculate an interval estimate.
 And, of course, always check that the method's assumptions and/or conditions are met.
Try it! Section
For each of the following research questions, identify at least one analysis that would be appropriate for the situation.

Do seniors earn higher semester grade point averages than freshmen?
Answer
We have two groups, seniors and freshmen. The response is continuous. We are only interested in determining whether or not a difference between the two groups exists. Therefore, conduct a twosample ttest for testing the difference in the mean GPA for seniors and the mean GPA for freshmen.

What is the relationship between the amount of alcohol consumed (in ounces) and the level of coordination (on a scale from 1 to 10)?
Answer
We have two continuous measurements, for which we are interested in quantifying the nature of the relationship. Therefore, conduct a linear regression analysis so that we can estimate:
\(\mu_y=\alpha + \beta x\)
where x denotes the amount of alcohol consumed and the level of coordination is the response y.

Are SAT scores and grade point averages linearly related?
Answer
We have two continuous measurements, for which we are interested in determining whether or not a linear relationship exists. Therefore, conduct a correlation analysis to test the null hypothesis:
\(H_0 : \rho = 0\)
against the alternative hypothesis:
\(H_A : \rho \ne 0\)

Is there a difference in the percentage of NCAA basketball players who graduate and NCAA football players who graduate?
Answer
The response is binary (graduate or not), and there are two groups being compared (NCAA basketball players and NCAA football players). Therefore, conduct a Ztest for comparing two proportions.

How many hours per week do PSU students study outside of class?
Answer
We have a continuous response variable (number of hours per week studied) and one group (PSU students). Therefore, calculate a onesample tinterval for the mean \(\mu\).

How much more prevalent is lupus in women than in men?
Answer
We have a binary response (lupus or not), and two groups (men and women). Therefore, calculate a Zinterval for the difference in the two proportions.

Do PSU students drink, on average, more than one cup of coffee per day during finals week? (During finals week, a sample of students will record how many cups of coffee they drink each day.)
Answer
We have a continuous response variable (number of cups of coffee consumed per day during finals week) and one group (PSU students). Therefore, conduct a onesample ttest for testing \(H_0: \mu = 1\) against \(H_A: \mu > 1\).

Is the recovery time from a migraine headache related to the treatment (A, B, C)?
Answer
We have a continuous response variable (recovery time) and three groups (A, B, C). Therefore, conduct a onefactor analysis of variance for testing \(H_0: \mu_A = \mu_B = \mu_C\) against \(H_A:\) not all \(\mu_i\) are equal.

Is there a relationship between political affilition (Democrat, Republican, Independent) and income level (Poor, Middle Class, Wealthy)?
Answer
We have two categorical variables for which we are interested in determining whether or not a relationship exists. Therefore, conduct a chisquare test.

How much heavier (in pounds) are 15yearold boys than 13yearold boys?
Answer
We have a continuous response (weight in pounds) and two independent groups (13yearold and 15yearold boys). Therefore, calculate a twosample tinterval for the difference in the two means.

A random sample of 64 students were asked "do you study regularly at Pattee Library?"
Answer
We have a binary response (yes or no) and one group (students). Therefore, calculate a confidence interval for the proportion of students who study regularly at Pattee.

Do Goodyear tires have better tread wear than Firestone tires? Tread wear is measured in millimeters of tread remaining after 30,000 miles. Thirty cars are selected for an experiment. On each car, one Goodyear tire and one Firestone tire is placed randomly in one of two front positions.
Answer
We have a continuous response (tread wear) and two paired groups (Firestone and Goodyear tires). Therefore, conduct a paired ttest for testing whether the mean difference is 0.