LANE Chapter 10 1. When would the mean grade in a class on a final exam be considered a statistic? When would it be considered a parameter? 2. Define bias in terms of expected value 3. Is it possible for a statistic to be unbiased yet very imprecise? How about being very accurate but biased? 4. Why is a 99% confidence interval wider than a 95% confidence interval? 5. When you construct a 95% confidence interval, what are you 95% confident about? 6. What is the difference in the computation of a confidence interval between cases in which you know the population standard deviation and cases in which you have to estimate it? 8. What is the effect of sample size on the width of a confidence interval? 9. How does the t distribution compare with the normal distribution? How does this difference affect the size of confidence intervals constructed using z relative to those constructed using t? Does sample size make a difference? 11. A population is known to be normally distributed with a standard deviation of 2.8. (a) Compute the 95% confidence interval on the mean based on the following sample of nine: 8, 9, 10, 13, 14, 16, 17, 20, 21. (b) Now compute the 99% confidence interval using the same data. 12. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future? 15. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. (a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean. (b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now? 16. You read about a survey in a newspaper and find that 70% of the 250 people sampled prefer Candidate A. You are surprised by this survey because you thought that more like 50% of the population preferred this candidate. Based on this sample, is 50% a possible population proportion? Compute the 95% confidence interval to be sure. ILLOWSKY - CHAPTER 8 PROBLEMS 49 - 61 (WORK ALL 13 OF THESE FOR 1 POINT) ALL ARE RELATED TO ONE SET OF DATA PRESENTED JUST BELOW QUESTION #48 IN THE ILLOWSKY TEST. DO THIS BY HAND, NOT SOFTWARE (EXCEPT FOR THE STD DEV IF YOU HAVE TO). Why would the error bound change if the confidence level were lowered to 95%? Use the following information to answer the next 13 exercises: The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X/ Freq. 1 /1 2 /7 3/ 18 4/ 7 5/ 6 49. Calculate the following: a. x =______ b. sx =______ c. n =______ 50. Define the random variable X in words. 51. What is x estimating? 52. Is x known? 53. As a result of your answer to Exercise #52, state the exact distribution to use when calculating the confidence interval. Construct a 95% confidence interval for the true mean number of colors on national flags 54. How much area is in both tails (combined)? 55. How much area is in each tail? 56. Calculate the following: a. lower limit b. upper limit c. error bound 57. The 95% confidence interval is_____. 59. In one complete sentence, explain what the interval means. 60. Using the same x , sx , and level of confidence, suppose that n were 69 instead of 39. Would the error bound become larger or smaller? How do you know? 61. Using the same x , sx , and n = 39, how would the error bound change if the confidence level were reduced to 90%? Why? 130. On May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S. workers believe that they willcontinue working past retirement age. The confidence level for this study was reported at 95% with a 3% margin of error. a. Determine the estimated proportion from the sample. b. Determine the sample size. c. Identify CL and . d. Calculate the error bound based on the information provided. e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values. f. Create a confidence interval for the results of this study. g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience