Examples of Tests of Significance and Power Calculations



Examples of Tests of Significance and Power Calculations

1) In each of the following situations a significance test for a population mean [pic]is called for. State the null and the alternative hypotheses.

a. Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus.

b. The examinations in a large accounting class are scaled after grading so that the mean score is 50. A self-confident teaching assistant thinks that his students have a higher mean score than the class as a whole. His students this semester can be considered a sample from the population of all students he might teach, so he compares their mean with 50.

c. A university gives credit in French language courses to students who pass a placement test. The language department wants to know if students who get credit in this way differ in their understanding of spoken French from students who actually take French courses. Some faculty think the students who test out the courses are better, but others argue that they are weaker in oral comprehension. Experience has shown that the mean score of students in the courses on a standard listening test is 24. The language department gives the listening test to a sample of 40 students who passed the credit examination to see if their performance is different.

2) The financial aid office of a university asks a sample of students about their employment and earnings. The report says that “for academic year earnings, a significant difference (P = 0.038) was found between the sexes, with men earning more on the average. No difference (P = 0.476) was found between the earnings of black and white students.” Explain both of these conclusions.

3) The survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude towards school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 20 students whar are least 30 years of age. Their mean score is [pic] = 135.2.

a. Assuming that [pic] = 30 for the population of older students, carry out a test of

[pic]

[pic]

Report the P-value of your test, and state your conclusion clearly.

b. Your test in (a) required two important assumptions in addition to the assumption that the value of [pic] is known. Which are they, which of them is most important for the validity of your conclusion?

4) To determine whether the mean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy group tests

[pic]

[pic]

The calculated test statistic is z = 2.42.

a. Is the result significant at the 5% level?

b. Is the result significant at the 1% level?

5) A SRS of 500 California high school students is used to test the following hypothesis about the mean SAT score:

[pic]

[pic]

Assume that the population standard deviation is [pic] = 100. The test rejects H0 at the 1% level when [pic]. Is this test sufficiently sensitive to usually detect an increase of 10 points in the population mean SAT score? Answer your question by calculating the power of the test against [pic] = 460.

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