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Confidence Intervals and Levels HW AP Statistics Name: _______________________ Date: _____________ Period: ____ Book Problems: Page 481 #3 - 9 odd, 10, 12, 16, 18 --------------------------------------------------------------------------------------------------------------------------------------------------1) Strictly speaking, what is the best interpretation of a 95% confidence interval for a population mean? (A) If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean. (B) A 95% confidence interval has a 0.95 probability of containing the true population mean. (C) 95% of the population distribution is contained in the confidence interval. (D) 95% of the time the sample statistic will be captured by the confidence interval generated. (E) 95% confident that the confidence interval was calculated correctly. 2) If the 90% confidence interval of the mean of a population is given by 45 ± 3.24, which of the following is correct? (A) There is a 90% probability that the true mean is in the interval. (B) There is a 90% probability that the sample mean is in the interval. (C) There is a 90% probability that a data value, chosen at random, will fall in this interval. (D) If 1000 samples of the same size are taken from the population, then approximately 900 of them will contain the true mean. (E) If 1000 samples of the same size are taken from a population, then approximately 900 will contain the sample mean. 3) Which of the following is not true about constructing confidence intervals? (A) The center of the confidence interval is the population parameter. (B) One of the values that affect the width of a confidence interval is the sample size. (C) If the value of the population parameter is known, it is irrelevant to calculate a confidence interval for it. (D) The value of the level of confidence will affect the width of a confidence interval. 4) The confidence that we feel about a 95% confidence interval comes from the fact that (A) There is a 95% chance that the population parameter is contained in the confidence interval. (B) There is a 95% chance that the sample statistic is contained in the confidence interval. (C) 95% of confidence intervals constructed around a sample statistic will contain the population parameter. (D) The terms confidence and probability are interchangeable. (E) The concepts of confidence and probability are synonymous. 5) A researcher plans to use a random sample of n = 500 families to estimate the mean monthly family income for a large population. A 99% confidence interval based on the sample would be ___________ then a 90% confidence interval. (A) Narrower and would involve a larger risk of being incorrect (B) Wider and would involve a smaller risk of being incorrect (C) Narrower and would involve a smaller risk of being incorrect (D) Wider and would involve a larger risk of being incorrect (E) Wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller 6) Two simple random samples of registered voters in a large city were taken. The first sample of 100 voters found that 50% of them were in favor of a new referendum that smoking is not permitted inside or on city property. The second sample of 400 voters also showed 50% in favor of the referendum. If two 95% confidence intervals were constructed based on these sample statistics, how would the width of the two intervals compare? Justify your results. 7) A friend who is taking AP Statistics at another school tells you that they did a problem in class whose answer was 95% confidence interval for a proportion of 0.35 ± 0.04. He says that the class agreed on the following interpretation of this interval: “There is a 95% chance that the true value of p is in this interval.” Describe how you would explain to your friend that this interpretation is wrong. Use for #8-11 From a sleep lab experiment, a 95% confidence interval for the mean number of hours that adults sleep at night is found to be (6.55,8.25). Of the statements below, identify if the statement is correct or incorrect. If you believe a statement is incorrect, explain why. 8) We are 95% confident that the true mean number of hours that adults sleep at night is between 6.55 and 8.25. 9) 95% of the confidence intervals we construct will give us the interval (6.55, 8.25). 10) There is a 95% probability that the mean number of hours that adults sleep is between 6.55 and 8.25. 11) We are 95% certain that the true mean number of hours that adults sleep is 7.4 + 0.85.