Random:the data come from a simple random sample of sales records.Large sample size: All theexpected counts (see part (b)) are at least 5.Independent: Individual observations of salesrecords within the random sample are independent; we must assume that there were more than1200 boxes of cereal sold.(d)222228122418617227189.51412187218;df =3;P-value 0.023 (UsingTable C, 0.02<P-value < 0.025).Since theP-value is less than= 0.05, we can rejectH0.There is convincing evidence that the distribution of size of boxes sold changed after the priceschanged.(e)It’s possible that we have made a Type I error, which is concluding that thedistribution of box sizes sold has changed when it has not.(f)Components of the chi-squarestatistic: Small: 1.33, Medium: 2.00, Large: 1.68, Jumbo: 4.5.The observed count of jumbo-sized boxes was much larger than the expected count, so it appears than an increase in sales ofjumbo-sized boxes was the biggest impact of the price changes.Quiz 11.1B1. 1.(a)H0: The distribution of blood types among performing arts students is the same as thedistribution among all U.S. residents.Ha:The distribution of blood types among performingarts students is different from the distribution among all U.S. residents.(b)Expected counts:Type A:0.4215063, Type B:0.1015015, Type AB:0.041506,Type O:0.4415066.(c)Random: the data come from a simple random sample of artsmajors and minors.Large sample size: All the expected counts (see part (b)) are at least 5.Independent: Individual observations of blood types within the random sample are independent;we must assume that there are more than 1500 students either majoring or minoring in arts at thislarge university.(d)222225063231510667669.6316315666;df =3;P-value 0.022 (UsingTable C, 0.02<P-value < 0.025).Since theP-value is less than= 0.05, we can rejectH0.There is convincing evidence that the distribution of blood type for performing arts students isdifferent from the U.S. distribution.(e)It’s possible that we have made a Type I error, which isconcluding that the distribution of blood types for arts majors and minors is different from theU.S. distribution when it is not different.(f)Components of the chi-square statistic: Type A: 2.68, Type B: 4.27, Type AB: 2.67, Type O:0.02.Type B blood made the largest contribution to the chi-square statistic, because theobserved count of arts students with Type B blood and Type AB blood were higher thanexpected by the null hypothesis.At the same time, the observed number of students with Type Ablood was lower than expected.This supports the claim that arts students are more likely to haveType B blood (perhaps Type AB as well).

534The Practice of Statistics, 4/e- Chapter 11© 2011 BFW PublishersQuiz 11.1C1.(a)State: We are testing the hypothesisHo: The proportion of sick day reports is the same forall five workdays, againstHa: At least one day’s proportionof sick day reports is different fromthe others.[Or:0:twhfHppppp, where eachpis the proportion of sick day calls ona day of the week, anda: at least of value ofpis not equal to the others.We will use asignificance level of= 0.05.Plan:mH

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