340 the practice of statistics 4e chapter 7 2011 bfw

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340The Practice of Statistics, 4/e- Chapter 7© 2011 BFW PublishersQuiz 7.2A1.(a)ˆˆ0.22;0.0589ppPV(b)0.30.022ˆ(0.30)(1.36)0.08690.0589P pPzP z±§·!!!¨¸©¹. (c)ˆpPwould not change,ˆpVwould be larger (0.073)and the distribution would be non-Normal,since³´³´130 0.26np±, which is less than 10.(d)The largest sample we can take is 50, otherwise the sample would be more than 10% of thepopulation, and sampling without replacement would require a finite population correction tocalculate standard deviation.2.(a)ˆˆ0.06;0.0336ppPV.(b)³´³´0.080.06ˆ0.080.600.27430.0336PpPzP z±§·!!!¨¸©¹.Quiz 7.2B1.(a)ˆˆ0.22;0.034ppPV(b) Since³´³´1500.223310nptand³´³´1150 .7811710np±t, the distribution is approximately normal.(c)ˆpPwould notchange,ˆpVwould be larger (0.069) and the distribution would be non-Normal, since³´36 0.227.92np, which is less than 10.(d)The largest sample we can take is 60, otherwise the sample would be more than 10% of thepopulation, and sampling without replacement would require a finite population correction tocalculate standard deviation.2.(a)ˆˆ0.20;0.025ppPV.(b)³´³´³´³´0.240.20ˆ0.241.580.05710.20.8250PpPzP z§·¨¸±¨¸!!!¨¸¨¸©¹.Quiz 7.2C1.(a)Since the probability of rolling a 1 or a 2 is 1/3, the mean of the sampling distribution is1/3.(b)ˆ12330.06160pV§·§·¨¸¨¸©¹©¹.(c)Since³´16020103np§·t¨¸©¹and³´216040103np§·±t¨¸©¹,the sampling distribution is approximately Normal.(d)³´³´0.50.33ˆ0.52.730.00320.061P pPzP z±§·!!!¨¸©¹.The probability of getting a sampleproportion as high or higher than 0.5 if the true proportion of rolling a die and getting a 1 or a 2is 0.33 is so small that it seems unlikely that the die is fair.2.(a)1520ˆ0.6082500p.(b)Thesample size (2500) is clearly less than 10% of the population (all adults);³´³´25000.6150010nptand³´³´12500 0.4100010np±t, so we can use the Normaldistribution to calculate this probability.We want to find³´ˆ0.608Pp!and then double it to
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 7341find the probability that a sample proportion is as far from 0.60 on either side of the Normalcurve.³´³´³´³´0.6080.6ˆ0.6080.820.20610.60.42500PpPzP z§·¨¸±¨¸!!!¨¸¨¸©¹times 2 = 0.4122.Quiz 7.3A1.(a)12xPminutes (the same as the population mean).(b) Yes.It seems reasonable toassume that the sample of 10 is less than 10% of the entire population calls.51.5810xV.(c)No.The population distribution is skewed, andn= 10, which is not large enough for thecentral limit theorem to apply.2.(a)³´³´4003804000.710.238928P xPzP z±§·!!!¨¸©¹(b)³´³´4003804001.240.1075283P xPzP z§·¨¸±¨¸!!!§·¨¸¨¸¨¸©¹©¹.(c)The mean weight of a random sample of three apples is less variable than the weight of asingle randomly-selected apple, so we are less likely to get a mean weight that is 20 gm abovethe mean when we take a sample of three apples.Quiz 7.3B1.(a)14000xPmiles (the same as the population mean).(b) Yes.It seems reasonable toassume that the sample of 12 is less than 10% of the entire population of customers.40001154.7012xV.(c)No.The population distribution is skewed, andn= 12, which is notlarge enough for the central limit theorem to apply.2.(a)³´³´5.57.55.51.600.05481.25P xPzP z±§·²

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