The Thematic Apperception Test (TAT) presents subjects with ambiguous pictures and asks then to tell a story about them. These stories can be scored in any number of ways. A group of researchers asked mothers of 10 children without and 10 children with depression to complete TAT and scored for the number of stories (out of 10) that exhibited a positive parent-child relationship. They wanted to know whether the mean TAT score for children with depression is lower than that for children without depression. Determine the null hypothesis for this test.?
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The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be? a. $H_{0} :$______ b. $H_{a} :$______
Hypothesis Testing with One Sample
Null and Alternative Hypotheses
Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We Dream in Color?” by Eva Murzyn, Consciousness and Cognition, Vol. 17, No. 4). We want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. An explanation given for the results is that those over the age of 55 grew up exposed to media that was mostly displayed in black and white. Can the results from parts (a) and (b) be used to verify that explanation?
Inference From Two Samples
Two Proportions
7–16. What’s the design? Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Depression The May 4, 2000, issue of Science News reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than non depressed people. Researchers studied 23 men and 48 women with major depression and 9 men and 24 women with no depression. They showed the subjects a sad film about a boy whose father has died, noting whether or not the subjects cried. Women cried more often than men, but there were no significant differences between the depressed and non depressed groups.
Gathering Data
Experiments and Observational Studies
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Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
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