A developmental psychologist compares 4-year-olds and 8-year-olds on their ability to understand the analogies used in stories. The scores for the five 4-year-olds tested were 7, 6, 2, 3, and 8. The scores for the three 8-year-olds tested were 9, 2, and 5. Using the .05 level, do older children do better?
(a) Use the steps of hypothesis testing.
(b) Sketch the distributions involved.
(c) Explain your answers to someone who understands the t test for a single sample but does not know anything about the t test for independent means.