Null Hypothesis Tests and Inferences About Means and Proportions

Topic 1
A tea-drinking friend of yours claims to have a very refined palate. She tells you that she can tell if, in preparing a cup of tea, milk is first added to the cup and then hot tea poured into the cup, or the hot tea is first poured into the cup and then the milk is added. To test her claims, you prepare six cups of tea. Three have the milk added first and the other three the tea first. In a blind taste test, your friend tastes all six cups and is asked to identify the three that had the milk added first. How many ways are there to select three of the six cups that had milk added first? If your friend is just guessing, what is the probability that she correctly identifies the three cups with the milk added first by chance?
Topic 2
Research suggests that pressure to perform well can reduce performance on exams. Are there effective strategies to deal with pressure? In an experiment, researchers had students take a test on mathematical skills. The same students were asked to take a second test on the same skills, but now each student was paired with a partner and only if both improved their scores would they receive a monetary reward for participating in the experiment. They were also told that their performance would be videotaped and watched by teachers and students. To help them cope with the pressure, 10 minutes before the second exam they were asked to write as candidly as possible about their thoughts and feelings regarding the exam. “Students who expressed their thoughts before the high-pressure test showed a statistically significant 5% math accuracy improvement (gain) from the pretest to posttest (P < .03).” A colleague who knows nothing about statistical reasoning says that an increase of 5% isn’t a lot—maybe it’s just an accident due to natural variation among the students. Explain in simple language how “P < .03” answers this objection."
Topic 3
Regarding Example 20.4 "Do Chimpanzees Collaborate?" the Conclusion states: The data give very strong evidence (p < .0005) that chimpanzees recruit a collaborator more often when faced with a problem that requires a collaborator to solve. That is, chimpanzees recognize when collaboration is necessary, a skill that they share with humans." Assume you saw this conclusion in a research article and wondered if the "strong evidence” refers to the small p-value in parentheses “(p < .0005). Reproduce the crosstab analysis in SPSS and run the chi-square test of independence. What results in the output corresponding to a description as "strong evidence?" Attach your SPSS output file to the discussion post.