Chapter 7 – Study Notes

 

1. What is a hypothesis?
2.  As the text suggests, study the example on pages 368-9.
3. What is the null hypothesis? What three forms can it take?
4. What is the alternative hypothesis? What three forms can it take?
5. If you are conducting a study and want to use a hypothesis test to support your claim, the claim must be worded so that it becomes the __________ hypothesis.
6. Sometimes, the _____________ hypothesis is referred to as the research hypothesis.
7. The flowchart on page 371 will help identify the different hypothesis.
8. The _____ _________ is a value computed from the sample data that is used in making the decision about the rejection of the null hypothesis.
9. The _________ _______ is the set of all values of the test statistic that cause us to reject the null hypothesis.
10. The _______ ______ is the probability that the test statistic will fall in the critical region when the null hypothesis is actually true.
11. A _______ ______ is any value that separates the critical region from the values of the test statistic that do not lead to the rejection of the null hypothesis.
12. The example on page 373 is very important, be sure to understand the difference between one-tailed and two-tailed hypothesis and tests.
13. Statistically, instead of accepting the null hypothesis – we will fail to reject the null hypothesis. What is the reasoning behind this wording?
14. The flowchart on the top of page 375 will be useful in wording the final conclusion.
15. What is a Type I error? What symbol is used to identify the probability of this type of error?
16. What is a Type II error? What symbol is used to identify the probability of this type of error?
17. Table 7-2 on page 376 will help to categorize these errors.
18. Type I  errors, Type II errors and _______ ______ are related. When the statistician chooses two of these, the third is determined.
19. The three possibilities are outlined on page 377 and the explanation about M&Ms and aspirin is very informative.
20. What is the ‘power of a test’? How is it calculated?
21. A power of at least ____ is a common requirement for determining that a hypothesis test is effective.

 

Do the odd problems on pages 378-381

 

22. What are the 3 methods of testing hypotheses about a mean?
23. What are the 3 assumptions about the tests? (page 381)
24. Data carelessly collected may be so completely useless that no amount of statistical __________ can salvage them.
25. What are the steps used to analyze the temperature data?
26. The text states that the histogram on page 382 is ‘roughly bell-shaped’, do you agree? Is there a requirement that the population data be bell-shaped (have a normal distribution)?
27. The chart on page 383 will help the student to understand the steps involved in using the traditional method of hypothesis testing.
28. You should feel comfortable with the calculations and discussion in the examples on pages 384 and 385
29. The approach used by the P-value method is to find the ___________ of getting a result.
30. The interpretations on the bottom of page 387 are important.
31. The P-value approach uses most of the same basic procedures as the ___________ approach, but Steps 6 and 7 are different.
32. The flowchart on page 389 will be helpful as you work through the P-value method.
33. Regarding the P-value discussion at the top of page 390, in many statistical reports, the P-value is often reported and the reader can judge for themselves if this is a significant result or not. It is common and usually expected for the statistician to report the P-values in reports.
34. Work through the examples on pages 390-1. Also, compare the calculations with those found in the previous examples (384-5) and how the methods are related.
35. Using the confidence interval method, we should _______ a claim that the population parameter has a value that is not included in the confidence interval.
36. For a two-tailed hypothesis test with significance level of alpha, use degree of confidence of _________. For a one-tailed hypothesis test with significance level of alpha, use degree of confidence of _________.
37. The procedure used to perform the test using STATDISK is given on page 393.

 

Work through the odd problems on pages 394-399

 

38. What are the assumptions concerning using small samples? How do these differ from those used for large samples?
39. What statistic is used to test the mean when the sample size is small and the standard deviation is unknown?
40. The flowchart on page 401 will help to decide which method to use when testing a claim about a population mean.
41. Read through the Pulse Rate example on page 402-3
42. The larger Student t critical value shows that with a small sample, the sample evidence must be more ________ before we consider the difference to be significant.
43. The example and discussion on page 404 help with the calculation of the p-values.

 

Work through the odd problems on pages 405-409

 

44. What are the assumptions for testing a claim about a proportion?
45. The Traditional Method and P-value methods are outlined on page 410.
46. Read through the example on page 411-13.
47. The technique used to calculate these values using STATDISK are given on page 413.

 

Work through the odd problems on pages 414-417

 

48. What are the assumptions concerning testing a claim about a standard deviation or variance.
49. A test that is robust is one that can still be accurate even if some of the assumptions are not met. Tests of claims about standard deviations or variances are not robust, meaning that the inferences can be misleading if the population does not have a normal distribution.
50. The _____ ______ statistic is used to test hypotheses about the standard deviation or variance.
51. Read through the example on pages 419-420. After obtaining the chi-square value, the P-value can be calculated.
52. The STATDISK technique is explained on page 421.

 

Work through the odd problems on pages 421-424.

 

Do the review and cumulative review exercises on pages 426-430.

 

MATH 1442 students need to:

1. Answer the 4 questions (Freshman 15) on page 425
2. The 3 questions (Critical Thinking) on page 433
3. Read Statistics at Work (page 434-5) and list the additional skills that Jeffrey Foy believes that are important for today’s college students
4. Throughout the past few chapters, quite a bit of the discussion has concerned the body temperature data. This information has been useful in that it has helped to illustrate the statistical techniques that we have been learning. However, one might have some concerns about the data used in this study. For example, we have already pointed out that only a few females are in the study. Also, the majority of the sample smokes. With this in mind, do you believe this to be a random sample? What evidence would you give to support your claim?

Email your answers to these questions to [email protected].

 

The Chapter 7 test will be available starting on ________ until _______. The test consists of 18 multiple choice questions and has a time limit of 40 minutes. You can use your textbook and notes as you take the test.