Question

For each of the following three scenarios, state which hypothesis test you would use from among the four: the z test, the single-sample t test, the paired-samples t test, and the independent-samples t test. Explain each answer in detail, including a discussion of the type of test, why it should be used, and the assumptions of the test.

A. A study of 40 children who had survived a brain tumor revealed that the children were more likely to have behavioral and emotional difficulties than were children who had not experienced such a trauma (Upton & Eiser, 2006). 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.

Answer 1

A:

Here we have single sample of 40 children and we need to compare their average with population mean. Since it is not given that population standard deviation is known so single sample t test will be used. Since sample size is large so assumption is needed.

B:

Here we have paired data for 54 students.

So paired t test should be used. Since sample size is large so assumption is needed.

C:

Here we have single sample and we need to compare sample mean with population mean and standard deviation is known so single sample z test will be used.

We need to assume that population under study is normally distributed.