328 CHAPTER 6 Confidence Intervals Extending Concepts Translating Statements In Exercises 29–34, translate the statement into a confidence interval. Approximate the level of confidence. 29. In a survey of 1502 U.S. adults, 31% said that they use Pinterest. The survey’s margin of error is {2.9%. (Source: Pew Research Center) 30. In a survey of 220 U.S. adults ages 18–29, 65% said that they use Snapchat. The survey’s margin of error is {7.9%. (Source: Pew Research Center) 31. In a survey of 1000 U.S. adults, 71% think teaching is one of the most important jobs in our country today. The survey’s margin of error is {3%. (Source: Rasmussen Reports) 32. In a survey of 880 unmarried U.S. adults who are living with a partner, 73% say love was a major reason why they decided to move in together. The survey’s margin of error is {4.8%. (Source: Pew Research Center) 33. In a survey of 2094 U.S. adults who have used an online dating app, 57% said their personal experience with online dating was positive. The survey’s margin of error is {3.6%. (Source: Pew Research Center) 34. In a survey of 1052 parents of children ages 8–14, 68% say they are willing to get a second or part-time job to pay for their children’s college education, and 42% say they lose sleep worrying about college costs. The survey’s margin of error is {3%. (Source: T. Rowe Price Group, Inc.) 35. Why Check It? Why is it necessary to check that nnp Ú 5 and nnq Ú 5? 36. Sample Size The equation for determining the sample size n = npnqa zc Eb 2 can be obtained by solving the equation for the margin of error E = zcBnpnq n for n. Show that this is true and justify each step. 37. Maximum Value of npnq Complete the tables for different values of np and nq = 1 - np. From the tables, which value of np appears to give the maximum value of the product npnq? np nq = 1 − np npnq 0.0 1.0 0.00 0.1 0.9 0.09 0.2 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 np nq = 1 − np npnq 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55
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