This assignment is putting all the three types of t test together to see if you can identify which t test should be used to answer specific research question (30 points in total). Please identify what t test you are going to use, and then follow the 4 steps of hypothesis testing to answer the questions.

A developmental psychologist is studying changes in creativity (cf. Terman, 1925; see Simonton, 2000, for a review). He collects scores on a divergent thinking test for third-graders and sixth-graders, and obtains the descriptive statistics below:

M s n

3rd Grade 75.00 5.00 26

6th Grade 80.00 7.00 16

Conduct the hypothesis testing at =0.05.

1. The first hypothesis he wants to test for is whether the third graders' average score differs significantly from that of the general population of children, which he knows is 72.00 (based on previous research). Are the divergent thinking skills of third graders in this sample significantly different from that of the general population? Conduct the appropriate statistical test and state your conclusion based on the data.

2. He then decides to compare scores on a divergent thinking test between third-graders and sixth-graders. Is 6th graders' score significantly better than that of 3rd grade? Develop and test a directional hypothesis regarding changes in creativity across childhood. Assume that the developmental psychologist obtained data using a cross-sectional design in one visit to a single school. Test your hypothesis and interpret your result.

3. Now assume instead that he obtained data from one cohort of 16 students, who were tested once when they were in 3rd grade and then again when they were in 6th grade. Retest your hypothesis from above using this longitudinal design.

M s n

3rd Grade 75.00 5.00 16

6th Grade 80.00 7.00 16

Difference(6th-3rd) 5.00 5.00

Note: the last row indicates the mean and standard deviation of difference scores are both 5.00.