Confidence Interval Quiz Review: Width & Adjustment of Intervals, Quizzes of Law

Download Confidence Interval Quiz Review: Width & Adjustment of Intervals and more Quizzes Law in PDF only on Docsity! Name: ________________________________ 1 Confidence Interval Quiz Review Your quiz tomorrow will be VERY much like this review! So FINISH IT!!! YOU KNOW WHO YOU ARE! :) 1. A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home-improvement stores. They select a simple random sample of 20 stores, record how many of the flashlights were sold in a 30-day period, and construct a 95% confidence interval for the mean number of flashlights sold. (a) If, instead of constructing a 95% confidence interval, the flashlight manufacturer constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain. (b) How would the width of confidence interval change if the flashlight manufacturer took a larger sample? Explain. (c) The 20 stores in the sample were actually the only stores who provided sales figures from 36 stores that were randomly chosen to be in the sample. Can the manufacturer adjust the confidence interval to take this nonresponse into account? If so, how? If not, why not? 2 2. A university health services physician is concerned about how much sleep freshman are getting in the first few months of school. She asks a simple random sample of 20 students how much sleep they got the previous night and constructs a 95% confidence interval for the mean amount of sleep in hours. (a) If, instead of constructing a 95% confidence interval, the physician constructed a 90% confidence interval, would the 90% interval be wider, narrower, or the same width as the 95% interval? Explain. (b) How would the width of confidence interval change if the physician took a larger sample? Explain. (c) After calculating the interval, the physician realizes that the sample was drawn only from the 70% of freshman who had turned in their health forms by the time they arrived on campus. Can she adjust the confidence interval to take this undercoverage into account? If so, how? If not, why not? 5 5. A recent poll found that “433 of the 1548 randomly-selected U.S. adults questioned felt that unemployment compensation should be extended an additional six months while the country is in its current economic downturn.” We want to use this information to construct a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way. (a) State the parameter our confidence interval will estimate. (b) Identify the conditions that must be met to use this procedure, and explain how you know that each one has been satisfied. (c) Find the appropriate critical value and the standard error of the sample proportion. (d) Give the 95% confidence interval. (e) Interpret the confidence interval constructed in part D. in the context of the problem. (f) Suppose you wanted to estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ± 1.5%. Calculate how large a sample you would need. 6 (g) If you wanted to have a margin of error of ±1.5% with 99% confidence, would your sample have to be larger, smaller, or the same size as the sample in part F.? Explain. (h) This poll was conducted by randomly calling cell phone numbers. Explain how undercoverage could lead to a biased estimate in this case, and speculate about the direction of bias. 6. A New York Times poll on women’s issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves. (a) Construct and interpret a 90% confidence interval that estimates the proportion of women in the United States who do not feel that they get enough time for themselves. Use the four-step process. (b) Explain, in the context of this problem, what “90% confidence” means. (c) Suppose this poll was conducted by telephone calls made from 9 am to 5 pm. Explain how using this method might result in biased results, and speculate about the direction of bias. 7 7. You want to conduct a poll at your school to estimate with 95% confidence the proportion of students in your school who have outside jobs in the evenings and on weekends. You’d like your margin of error to be less than ±5%. (a) How large must your sample be to produce a 95% confidence interval with the desired margin of error of ±5%? (b) How big does your school have to be for this interval to be accurate? Explain.