Math 370 HW 7 - Homework 7 Solution 5-3 (a, c), 5-8, 5-19,...

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1Homework 7 Solution5-3 (a, c), 5-8, 5-19, 5-20, 5-37, 5-385-3a) 1) The parameter of interest is the difference in fill volume,122) H0:120or123) H1:120or124) The test statistic iszxxnn0120121222()5) Reject H0if z0<z/2=1.96 or z0> z/2= 1.966)x116.015x216.005= 010.0320.025n1= 10n2= 1081.010)025.0(10)03.0(0)005.16015.16(220z7) P-value =418.0)7910.01(2))81.0(1(2Because the P-value is > 0.05, fail to reject the null hypothesis. There is not sufficient evidence to conclude that themeans of the two fill volumes are different at= 0.05.b) Power =1 , whereznnznn//2012122220121222=10)025.0(10)02.0(04.096.110)025.0(10)02.0(04.096.12222=91.599.195.396.195.396.1= 0.02330= 0.0233
2Power = 10.0233 = 0.977c)xxznnxxznn12212122212122121222//16 01516 0051960 02100 0251016 01516 0051960 02100 02510221222...( .)( .)...( .)( .)000980029812..With 95% confidence, the difference in the mean fill volumes is between0.0098 and 0.0298. Because 0 is containedin this interval, we can conclude there is no significant difference between the means.d) Assume the sample sizes are to be equal, use= 0.05,= 0.01, and= 0.04,08.2)04.0()025.0()02.0(33.296.1zzn22222222122/n = 11.79, use n1= n2= 125-8.x188.85x292.54121.5

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