Question: For each of the following three scenarios, state which hypothesis test you would use from among the four introduced so far: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. (Note: In the actual studies described, the researchers did not always use one of these tests, often because the actual experiment had additional variables.) Explain your answer.

a. A study of children who had survived a brain tumor revealed that they were more likely to have behavioral and emotional difficulties than were children who had not experienced such a trauma (Upton & Eiser, 2006). Forty families in which a child had survived a brain tumor participated in the study. Parents rated children's difficulties, and the ratings data were compared with known means from published population norms.

b. Talarico and Rubin (2003) recorded the memories of 54 students just after the terrorist attacks in the United States on September 11, 2001-some memories related to the terrorist attacks on that day (called flashbulb memories for their vividness and emotional content) and some everyday memories. They found that flashbulb memories were no more consistent over time than everyday memories, even though they were perceived to be more accurate.

c. The HOPE VI Panel Study (Popkin & Woodley, 2002) was initiated to test a U.S. program aimed at improving troubled public housing developments. Residents of five HOPE VI developments were examined at the beginning of the study so researchers could later ascertain whether their quality of life had improved. Means at the beginning of the study were compared to known national data sources (e.g., the U.S. Census, the American Housing Survey) that had summary statistics, including means and standard deviations.