1. Ehlers, Maercker, and Boos studied various characteristics of political prisoners from the former East Germany and presented their ndings in the paper \"Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of mental Defeat. Alienation and Perceived Permanent Change\". According to the article, the mean duration of imprisonment for 32 patients with chronic PTSD was 33.4 months. Assuming that o = 42 months, a 99% condence interval for the mean duration ofimprisonment, p, of all East German political prisoners with chronic PTSD is [14.27, 52.53]. a) If we wanted to have a more precise interval (decrease the width) would we need to increase or decrease our confidence level? b) If we wanted to have a more precise interval (decrease the width) would we need to increase or decrease our sample size? c) Can we change the width of our condence interval by changing the population standard deviation? Explain. d) Based on the 99% condence interval [14.27, 52.53] can we conclude at alpha:.01 that the mean duration of imprisonment for patients with chronic PTSD is different than 14 months? Explain. 2. What are the strengths and weaknesses of doing a hypothesis test, versus calculating a condence interval? 3. The average cost oftextbooks for sociology courses at KU is $1 19.25. You randomly ask 15 sociology majors what the average cost oftextbooks for their sociology courses is and you nd that 65% ofthem spent more than this amount. a) is $1 1925 a parameter or a statistic? b) is 65% a parameter or a statistic? 4. A bottling company uses a lling machine to fill plastic bottles with a popular cola. The contents ofthe bottles vary according to a normal distribution with a mean u = 298 ml and o = 4 m]. a) What is the probability that the mean contents ofa simple random sample off) bottles is more than 300 m1? b) What is the probability that a randomly selected bottle has more than 300 m1? c) What are the mean and standard deviation ofthe sample mean when n=6? (1) How large a sample would be needed to reduce the standard deviation ofthe sample mean to 0.5 ml? 5. The average level of calcium in the blood of healthy young adult females in Guatemala is 9.5 milligrams per deciliter. A clinic in rural Guatemala measures the blood calcium level of 160 healthy pregnant women in their first visit for prenatal care. The mean for this sample is 9.57. Assume the population standard deviation is 0.4. Is this an indication that the mean calcium level in healthy pregnant women is different than 9.5 milligrams per deciliter? Use alpha=.05 ' ' 6. True or False a) T F When calculating a 95% confidence interval from a stratied sample we can be 95% confident that the true pOpuiation mean falls in this interval. b) T F At alpha=.05 a p-value of .04 is stronger evidence against the null than a p-value of .02 because .04 is closer to .05. c) T F Larger pvalues will be required to convince someone with strongly held beliefs that their beliefs are wrong. d) T F Smaller p-values will be required to reject the null when the consequences of rejecting the null are expensive or harmful. e) T F The p-value represents the probability that the null is true. i) T F Statistical software reports two-tailed signicance tests because they are more conservative and provide stronger evidence against the null. g) T F You should hypothesize a one-tailed test if your sample data show a mean that is above or below the mean in your null hypothesis. h) T F The standard cut-off level for statistical signicance is .05. i) T F When we fail to reject the null the results are statistically signicant. 0) T F The sampling distributions for a statistic will be approximately normal with large sample sizes even when the population distribution is skewed. p) T F 2 procedures are sensitive to outliers. q) T F The p-value is the probability the null is true given our test statistic. r) T F If you do 100 signicance tests at alpha=.05 and the null is true, approximately 5 of these would be statistically signicant just due to chance. 5) T F The sampling frame is what you call the list of people who participated in your study. t) T F The p-value represents the probability that we would observe our data (or data more extreme) assuming the null hypothesis was true. 7. What is wrong with the following statement: Assuming the same mean and standard deviation in the population, sampling distributions have more variability when samples are taken from small populations than when they are taken from large populations. 8. A re insurance company felt that the mean distance from a home to the nearest re department in a suburb of Chicago was 4.7 miles, and set its re insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they felt, would convince the insurance company to lower its rates. They randomly identied 64 homes and measured the distance to the nearest re department for each. The resulting sample mean was 4.4 miles. Assume the standard deviation for the population is 2.4 miles. a) Does the sample show sufcient evidence to support the communities claim at the alpha=0.05 level of signicance? b) Calculate a 96% condence interval for the mean distance from a home to the nearest re department in this suburb of Chicago. Interpret the condence interval in a complete sentence. c) The insurance company wants the community to be able to estimate the true population mean to within 0.25 miles with 99% condence. How many homes would they have to survey to meet this requirement? 9. Does statistical signicance tell us whether an effect is large enough to be important? Explain