Statistical Analysis of Experimental Results

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Statistical Analysis of Experimental ResultsChapter 4, Section 3, Exercise 075SSMatch thep-values with the appropriate conclusion:(a) The evidence against the null hypothesis is significant, but only at the10%level.0.0883(b) The evidence against the null and in favor of the alternative is very strong.0.00013(c) There is not enough evidence to reject the null hypothesis, even at the10%level.0.6251(d) The result is significant at a5%level but not at a1%level.0.0219Chapter 4, Section 3, Exercise 082Sleep or Caffeine for Memory?The consumption of caffeine to benefit alertness is a common activity practiced by90%of adults in North America. Often caffeine is used in order to replace the need for sleep.One recent study1compares students' ability to recall memorized information aftereither the consumption of caffeine or a brief sleep. A random sample of35adults(between the ages of18-39) were randomly divided into three groups and verballygiven a list of24words to memorize. During a break, one of the groups takes a nap foran hour and a half, another group is kept awake and then given a caffeine pill an hourprior to testing, and the third group is given a placebo. The response variable of interestis the number of words participants are able to recall following the break. The summarystatistics for the three groups are in the table below. We are interested in testingwhether there is evidence of a difference in average recall ability between any two of thetreatments. Thus we have three possible tests between different pairs of groups: Sleepvs Caffeine, Sleep vs Placebo, and Caffeine vs Placebo.GroupSample sizeMeanStandard

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DeviationSleep1215.253.3Caffeine1212.253.5Placebo1113.703.01Mednick, Cai, Kanady, and Drummond, "Comparing the benefits of caffeine, naps andplacebo on verbal, motor and perceptual memory",Behavioural Brain Research, 193(2008), 79-86.Don't show me this message again for the assignment(a) In the test comparing the sleep group to the caffeine group, thep-value is0.003.What is the conclusion of the test?RejectH0.In the sample , which group had better recall ability?SleepAccording to the testresults, do you think sleep is really better than caffeine for recallability?YesDon't show me this message again for the assignment(b) In the test comparing the sleep group to the placebo group, thep-value is0.06.What is the conclusion of the test, using a5%significance level?Do not rejectH0.

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What is the conclusion of the test, if we use a10%significance level?RejectH0.How strong is the evidence of a difference in mean recall ability between these twotreatments?No evidence at allDon't show me this message again for the assignment(c) In the test comparing the caffeine group to the placebo group, thep-value is0.22.What is the conclusion of the test?Do not rejectH0.In the sample , which group had better recall ability?PlaceboAccording to the test results, would we be justified in concluding that caffeine impairsrecall ability?NoDon't show me this message again for the assignment(d) According to this study, what should you do before an exam that asks you to recallinformation?

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Take anap.Have a placebo.Have some coffee.Don't show me this message again for the assignmentChapter 4, Section 4, Exercise 128Arsenic in ChickenA restaurant chain is measuring the levels of arsenic in chicken from its suppliers. Thequestion is whether there is evidence that the mean level of arsenic is greater than80ppb, so we are testingH0:=80vsHa:>80, whererepresents the average level ofarsenic in all chicken from a certain supplier. It takes money and time to test for arsenicso samples are often small. Supposen=6chickens from one supplier are tested, and thelevel of arsenic (in ppb) are63,71,82,92,93,139.Don'tshow me this message again for the assignment(a) What is the sample mean for the data?Round your answer to the nearest integer.x=90

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Don't show me this message again for the assignmentthe tolerance is +/-2%(b) Translate the original sample data by the appropriate amount to create a new dataset in which the null hypothesis is true. How do the sample size and standard deviationof this new data set compare tothe sample size and standard deviation of the originaldata set?They are different.The sample size is the same but the standard deviation is different.The standard deviation is the same but the sample size is different.They are thesame.Don't show me this message again for the assignment(c) Write the six new data values from part (b) on six cards. Sample from these cardswith replacement to generate one randomization sample. (Select a card at random,record the value, put it back, select another at random, until you have a sample size of6, to match the original sample size.) Give the sample mean.x=73.833Don't show me this message again for the assignmentthe tolerance is +/-2%

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Chapter 4, Section 5, Exercise 149Hypotheses for a statistical test aregiven, followed by several possible confidence intervalsfor different samples. In each case, use the confidence interval to state a conclusion of thetest for that sample, and give the significance level used. In addition, in each case for whichthe results are significant, state which group (1or2) has the larger mean.Hypotheses:H0:1=2vsHa:1≠2(a)95%confidence interval for :1-2: 0.16to0.58Conclusion:RejectH0Significance level:5%Group with the larger mean:Group 1(b)99%confidence interval for1-2:-2.5to5.5Conclusion:Do not rejectH0Significance level:1%Group with the larger mean:Cannot determine(c)90%confidence interval for1-2:-10.8to-3.3Conclusion:RejectH0Significance level:10%Group with the larger mean:Group 2Chapter 4, Section 5, Exercise 156

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