Chapter 6 – Study Notes

 

1. ____________ statistics are used to summarize important characteristics of data, while _______________ statistics are used to make generalizations about a population.

2. What are the two major applications of inferential statistics?

3. The book gives 4 suggestions to help the student understand the material in this section, what are these 4 suggestions?

4. What are the two assumptions for estimating a population mean using large samples?

5. Data collected _______ can be absolutely _______, even if the sample is quite large.

6. If you collect data from your friends, would you classify this data as random or biased?

7. What is an estimator? An estimate? A point estimate?

8. The ______________ is the best point estimate of the population mean. (The Greek letter for ‘u’ is called ‘mu’.) What are some other point estimates that could be used to estimate the population mean?

9. Why does the sample mean provide the best estimate?

10. In the example on page 298, it concludes that the best point estimate of the population mean is a temperature of 98.20 degrees. The raw data is in Appendix B – Data set 6 – page 785-7. Look at this data – do you consider this to be a random sample or a biased sample? In a random sample, how many females would you expect? What is the youngest age? The oldest? Is there much variation across days?

11. What is a confidence interval?

12. The value of alpha is the complement of the degree of confidence. For a 0.95 (or 95%) degree of confidence, alpha = 0.05. For a 0.99 (or 99%) degree of confidence, alpha – 0.01.

13. What are the three most common choices of confidence intervals?

14. The explanation given in the section INTERPRETING A CONFIDENCE INTERVAL gives a good explanation of a complex and sometimes confusing concept.

15. With 95% confidence, we would expect ____ of 20 samples should result in confidence intervals that do contain the true value of the population mean.

16. What is a CRITICAL VALUE? What are the five observations given on pages 300-1?

17. The critical values given on page 302 will be used repeatedly through the remainder of the course. Copy them and put them in a place where you can refer to them easily.

18. What is the ‘margin of error’?

19. The three ways to present the Confidence Interval are just three different ways to say the same thing – the definition gives a good summary of all of these.

20. The example on page 304 will help you to understand more about Confidence Intervals.

21. The formulas on page 305 will help if you need to calculate the sample mean but all you know is the upper and lower confidence interval limits. The other formula gives the calculation for the margin of error.

22. The confidence interval can be calculated fairly easily with a calculator, but you should also be able to do it with STATDISK – the instructions are on page 308.

 

Work the odd problems on pages 309-312

 

23. What are the 3 assumptions associated with using a small sample size? If the first assumption is false, what is the alternative? If the second assumption is false, what can be done? If the third assumption is false, what can be done?

24. Which of the two cases on page 313 is the most likely to occur?

25. What is the formula used to calculate the ‘t’ value?

26. What are ‘degrees of freedom’?

27. How is the margin of error calculated?

28. Five properties of the Student t distribution are given on page 316.

29. The flowchart on page 317 will help you make decisions about which statistic to use.

30. The point of the discussion on page 318 is that a statistician can use the normal distribution IF they know the standard deviation of the population BUT that is rarely the case – so, the Student t distribution is used the majority of the time.

31. The examples on page 318-9 are helpful.

32. Again, work through the STATDISK example on page 319.

 

Do the odd problems on page 320-323

 

33. On page 323, a formula is given for calculating the sample size needed to estimate the Mean. What three factors does this formula depend upon?

34. What is the round-off rule for sample size?

35. Refer to question 33 – which of these factors is usually unknown?

36. What are some methods that can be used to work around the problem listed in question 35?

37. When calculating the sample size, is it better to get a sample that is too large or too small?

38. The example on page 325 will help the student to understand the calculations.

39. Doubling the margin of error causes the required sample size to decrease to ____ of the original value.

40. Since large samples generally require more time and money, there is often a need for a trade-off between the ________ ______ and the ________ ___ _________.

41. The instructions at the bottom of 326 will help explain how to use STATDISK to calculate sample size.

 

Do the odd problems on page 327-329

 

42. What is ‘p hat’?

43. 48.7% is the same as 0.487.

44. The sample proportion ____ is the best point estimate of the population proportion p.

45. What is the formula for the margin of error for the estimate of p? The confidence interval?

46. Based on the information given in the example (Misleading Survey Responses) on page 332-3, would you agree or disagree with the conclusion?

47. When determining the sample size, the text states that ‘p hat’ and ‘q hat’ can be replaced by 0.5. What is the rationale behind this? (Hint: calculate p hat times q hat for several different values – where is the result the greatest? For example, 0.4 X 0.6 yields 0.24, 0.3 X 0.7 yields 0.21, etc. Also, refer to previous study question 37.)

48. What are some of the common errors made when calculating the sample size?

49. The instructions on page 337 explain how to use STATDISK to calculate confidence intervals.

50. Work through the odd problems on page 337-342.

51. The Normal and Student t distribution are used when estimating _______ and ______________. The chi-square distribution is used when estimating __________ and _______________ _________________.

52. What is the formula for chi-squared?

53. Why do separate calculations have to be done for the upper and lower confidence intervals of a chi square?

54. The example on page 345 helps explain the steps involved in calculating the confidence intervals for a chi-square distribution.

55. The calculations for the Right and Left confidence intervals for the variance are given on page 346.

56. The example on page 348 explains how to calculate the confidence interval on the variance of the body temperature data.

57. The procedure used to calculate sample size using STATDISK is given on 349.

58. The Table on page 350 will be used instead of calculations for the sample size needed to estimate the population variance.

59. The steps used to calculate the confidence intervals using STATDISK are given on page 350.

 

Do the odd problems on page 351-3.

 

Do the review exercises and cumulative review exercises on pages 355 to 358.

 

Students enrolled in MATH 1442 need to answer the 4 questions on page 354 and the 3 questions on page 360. Also, read the Statistics at Work article on pages 362-3 and list 5 skills that standout college graduates should have. Email your answers to these questions to [email protected]

 

The Chapter 6 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 exam.