# 9 we should examine the data since the normality of

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= 9, we should examine the data,since the normality of the population isimportant.The dotplot at right is reasonably symmetric and shows no evidence of strong skewor outliers.We should be safe using t-procedures.Independent: It seems reasonable to assumethat individual samples of soil are independently selected, and that we are sampling less than10% of the contaminated soil.
Do:Critical t for 90% confidence and 8 df is 1.860,so the 90% confidence interval is0.1581.0761.861.0760.0980(0.978,1.174)9§·roro¨¸©¹.Conclude (i.e., interpret the interval):We are 90% confident that the interval 0.978 to 1.174 contains the true mean degradation rate bythese fungi.Since some of this interval is below 1.00, we cannot be confident that thedegradation rate is greater than 1.00, so the methods may not be cost-effective.
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 8397Quiz 8.3C1.C is narrower than A, A is narrower than B.Fort-intervals, critical values for any specificconfidence level decrease as the degrees of freedom increases.Az-interval is equivalent to at-interval with ―infinite‖ degrees of freedom.2.We want a sample sizensuch that±²201.964n§·d¨¸©¹.Solving as an equality producesn= 96.04, sonshould be 97.3.(a)Thedistribution is moderately skewed right, but sincen= 30, we should be safe usingt-proceduresbecause of the central limit theorem.(b) The distribution has a moderate-to-strong right skewand maximum value is close to meeting the 1.5 x IQR rule for outliers.Moreover, the samplesize is small.It is not advisable to uset-procedures with this sample.(c)The distribution isstrongly skewed right, but there are no outliers, andn= 45.We should be safe usingt-procedures because of the central limit theorem.4.(a)1.230.225.30sn|If many samplesof this size were taken, the difference between a sample mean score and the population meanscore would be, on average, about0.225.(b)State:We wish to estimate, with 99%confidence, the true mean score on this AP Statistics question.Plan:We will use a one-samplet-interval for a population mean.Conditions:Random:The study refers to a random sample.Normal:We concluded in the previous question that we should be safe usingt-procedures.Independent: It seems reasonable to assume that individual student scores are independentlyselected, and we are clearly sampling less than 10% of the population.Do:Criticaltfor 99%confidence and 29 df is 2.756, so the 99% confidence interval is1.231.2672.7561.2670.619(0.648,1.886)30§·roro¨¸©¹.Conclude (i.e., interpret the interval):We are 99% confident that the interval 0.648 to 1.886 contains the true mean score on thisquestion.
398The Practice of Statistics, 4/e- Chapter 8© 2011 BFW PublishersTest 8APart 11.b±²±²0.250.750.0306200|2.dWhile this is a probability sample of sorts, it is not a random sample that is representativeof the population.Because he sampled for only one two-hour period, the sample issubject to bias arising form the specific day and time he sampled.

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