Two machines are used to fill plastic bottles with dishwashing detergent. The st

Question

Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be sigma_1 = 0.10 and sigma_2 = 0.15 fluid ounces for the two machines, respectively. Two random samples of n_1 = 12 bottles from machine 1 and n_2 = 9 bottles from machine 2 are selected, and the sample mean fill volumes are X^-_1 = 30.61 and X^-_2 = 30.44 fluid ounces. Assume normality. Test the hypothesis that both machines fill to the same mean volume. Use the P-value approach. Round your answer to 3 decimal places.

Explanation / Answer

H0: 1 = 2
Ha: 1 2

n1 = 12, n2 = 9, 1 = 0.1, 2 = 0.15, xbar1 = 30.61, xbar2 = 30.44

Standard Error, SE = sqrt[ (12/n1) + (22/n2) ] = sqrt(0.12/12 + 0.152/9) = 0.05773503

Z = ((xbar1 - xbar2)-0)/ SE = ((30.61-30.44)-0)/0.05773503 = 2.944486373

For =0.05, zc=1.96, since z > zc, nul hypothesis is rejected

p-value is p = 0.003, and since p = 0.003 < 0.05, it is concluded that the null hypothesis is rejected.

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