hw6_solution_stat425 - STAT 425 FALL 2015 Section T1U T1G...

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STAT 425 - FALL 2015 - Section T1U, T1GHomework VI SolutionNovember 25, 2015Problem 1(a)The summary of the Helium Football data is given in Listing 1 and in Figure 1.Listing 1: Summary R outputTrialAirHeliumDiffMin.:1.0Min.:15.00Min.:11.00Min.: -14.00001stQu .:10.51stQu .:23.501stQu .:24.501stQu.:-2.0000Median:20.0Median:26.00Median:28.00Median:1.0000Mean:20.0Mean:25.92Mean:26.38Mean:0.46153rdQu .:29.53rdQu .:28.503rdQu .:30.003rdQu.:4.0000Max.:39.0Max.:35.00Max.:39.00Max.:17.0000(b)The summary of the appropriate t-test (one sample) is given in Listing 2.We fail to reject thenull here, that is there is no significant difference in the distance kicked for the two balls.Listing 2: Summary R outputOneSamplet-testdata:Difft=0.4198 ,df=38,p-value=0.677alternativehypothesis :truemeanisnotequalto095percentconfidenceinterval:-1.7643462.687423sampleestimates :meanofx0.4615385(c)We perform the approximate randomization test with 100000 iterations. The approximate p-valueis0.69538. So our conclusions do not change.(d)The histogram of the randomization distribution of the t-statistic based on our previous simula-tion is given in Figure 2.Problem 2(a)There are 4 blocks and 12 experimental units in the eggprod data.

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