Copyright © Cengage Learning. All rights reserved. 8 Tests of Hypotheses Based on a Single Sample

Copyright © Cengage Learning. All rights reserved. 8.4 Tests Concerning a Population Proportion

3 Let p denote the proportion of individuals or objects in a population who possess a specified property (e.g., college students who graduate without any debt, or computers that do not need service during the warranty period). If an individual or object with the property is labeled a success (S), then p is the population proportion of successes. Tests concerning p will be based on a random sample of size n from the population.

4 Large-Sample Tests

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10 Large-Sample Tests

11 Large-Sample Tests

12 Example 8.13 Student use of cell phones during class is perceived by many faculty to be an annoying but perhaps harmless distraction. However, the use of a phone to text during an exam is a serious breach of conduct. The article “The Use and Abuse of Cell Phones and Text Messaging During Class: A Survey of College Students” (College Teaching, 2012: 1–9) reported that 27 of the 267 students in a sample admitted to doing this. Can it be concluded at significance level.001 that more than 5% of all students in the population sampled had texted during an exam?

13 Example 8.13

14 Example 8.13

15 Example 8.13

16 β and Sample Size Determination

17 β and Sample Size Determination

18 β and Sample Size Determination

19 Example 8.14

20 Example 8.14

21 Example 8.14

22 Small-Sample Tests

23 Small-Sample Tests

24 Small-Sample Tests

25 Small-Sample Tests

26 Example 8.15 A plastics manufacturer has developed a new type of plastic trash can and proposes to sell them with an unconditional 6-year warranty. To see whether this is economically feasible, 20 prototype cans are subjected to in accelerated life test to simulate 6 years of use. The proposed warranty will be modified only if the sample data strongly suggests that fewer than 90% of such cans would survive the 6-year period.

27 Example 8.15

28 Example 8.15 From Appendix Table A.1, B(15; 20,.9) 5.043, whereas B(16; 20,.9) The closest achievable significance level to.05 is therefore.043. Since B(14; 20,.9) 5.011, H0 would be rejected at this significance level if the accelerated test results in x = 14. It would then be appropriate to modify the proposed warranty.

29 Example 8.15