In what way?(e) If you took a sample of 50 individuals instead of 100 from the original community, wouldthe sampling distribution of the statistic change?In what way?

308The Practice of Statistics, 4/e- Chapter 7© 2011 BFW Publishers2.Below are histograms of the values taken by three sample statistics in several hundredsamples from the same population.The true value of the population parameter is marked oneach histogram.(a)Which statistic has the largest bias among these three?Justify your answer.(b)Which statistic has the lowest variability among these three?Justify your answer.(c)Based on the performance of the three statistics in many samples, which is preferred as anestimate of the parameter?Why?

© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 7309Quiz 7.2AAP StatisticsName:1.According to the 2000 U.S. Census, 80% of Americans over the age of 25 have earned a highschool diploma.Suppose we take a random sample of 120 Americans and record theproportion, ˆ,pof individuals in our sample that have a high school diploma.(a) What are the mean and standard deviation of the sampling distribution of ˆ ?p(b) What is the approximate shape of the sampling distribution? Justify your answer.(c) Suppose our sample size was 30 instead of 120.Compare the shape, center, and spreadof this sampling distribution to the one in parts (a) and (b).(d)You live in a small town with only 500 residents over the age of 25.What is the largestpossible sample you can take from your town and still be able to calculate the standarddeviation of sampling distribution ofˆpusing the method presented in the textbook?Explain.

310The Practice of Statistics, 4/e- Chapter 7© 2011 BFW Publishers2.George is a big fan of music from the 1960s, and 22% of the songs on his mp3 player areBeatles songs.Suppose George sets his mp3 player to “shuffle,” so that it selects songsrandomly (assume the shuffle function permits repetition of songs).During a long drive,George plays 50 randomly-selected songs.(a) What are the mean and standard deviation of the proportion of the 50 randomly-selectedsongs that are Beatles songs?(b) Calculate the probability that more than 30% of the 50 randomly-selected songs areBeatles songs.

© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 7311Quiz 7.2BAP StatisticsName:1.According to a poll, 22% of high school students in the United Kingdom say that Dobby istheir favorite character in the Harry Potter books.Let’s assume this is the parameter valuefor the entire population of high school students in the U.K.You take a sample of 150 highschool students and record the proportion, ˆ,pof individuals in your sample who say Dobby istheir favorite character.(a) What are the mean and standard deviation of the sampling distribution of ˆ ?p(b) What is the approximate shape of the sampling distribution? Justify your answer.(c) Suppose our sample size was 36 instead of 150.Compare the shape, center, and spreadof this sampling distribution to the one in parts (a) and (b).(d)A small town in the U.K. has only 600 high school students.

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