# Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The...  Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed normal, with standard deviation o1 = 0.020 and 02 = 0.025 ounces. A member of the quality engineering staff suspects that both machines fill to the same mean net volume, whether or not this volume is 16.0 ounces. A random sample of 10 bottles is taken from the output of each machine Machine 1 16.03 16.01 16.04 15.96 16.05 15.98 16.05 16.02 16.02 15.99 Machine 2 16.02 16.03 15.97 16.04 15.96 16.02 16.01. 16.01 15.99 16.00 Find the upper bound of a 95% Cl on the difference of means Use at least 2 decimal digits
The manager of a fleet of automobiles is testing two brands of radial tires. She assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data are shown here (in kilometers). Find the lower bound of a 99% Cl on the difference in mean life Car Brand 2 Car Brand 1 Brand 2 36.925 34 318 2 45.300 42.280 36.240 35.500 4 32.100 31.950 5 6 Brand 1 37.210 48,360 38.200 33.500 38,015 47,800 37.810 33.215 8 Use two decimal digits

1)

 X1 bar 16.015 (AVERAGE()) X2 bar 16.005 S1 0.02 (GIVEN) S2 0.025 n1 10 n2 10
 95%CI α = 0.05 Zc 1.959964 +/-   NORM.S.INV(α/2) ME 0.019843 Zc*SQRT(S1^2/n+S2^2/n) Upper 0.029843 (X1 bar-X2 bar) + Zc*SQRT(S1^2/n+S2^2/n) Lower -0.00984 (X1 bar-X2 bar) - Zc*SQRT(S1^2/n+S2^2/n)

Upper bound = 0.03

2)

 Sample1 Sample 2 Diff 36925 34318 2607 45300 42280 3020 36240 35500 740 32100 31950 150 37210 38015 -805 48360 47800 560 38200 37810 390 33500 33215 285 Mean Dbar 868.375 Sd Sd 1290.033 n 8
 99% CI α = 0.01 tc 3.499483 T.INV.2T(alpha,df) ME 1596.099 tc*(Sd/SQRT(n)) Upper 2464.474 D bar + tc*(Sd/SQRT(n)) Lower -727.724 D bar - tc*(Sd/SQRT(n))

Lower bound = -727.72

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