1. Two machines are used to fill plastic bottles with dishwashing detergent. The
ID: 3225197 • Letter: 1
Question
1. Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be 1 = 0.11 fluid ounces and 2 = 0.16 fluid ounces for the two machines, respectively. Two random samples of n1 = 12 bottles from machine 1 and n2 = 10 bottles from machine 2 are selected, and the sample mean fill volumes are = 30.87 fluid ounces and = 30.68 fluid ounces. Assume normality. We test the hypothesis that both machines fill to the same mean volume.
1-3. We are now wondering if Machine 1 fills to more volume than Machine 2. Construct a 90% lower-confidence interval on the mean difference in fill volume. Conclude with this interval.
PLEASE SHOW ALL WORK. I NEED A 90% LOWER CONFIDENCE INTERVAL ON THE MEAN DIFFERENCE IN FILL VOLUME!!!!!
Explanation / Answer
n1 = 12
n2 = 10
x1-bar = 30.87
x2-bar = 30.68
s1 = 0.11
s2 = 0.16
% = 90
Degrees of freedom = n1 + n2 - 2 = 12 + 10 -2 = 20
Pooled s = (((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = (((12 - 1) * 0.11^2 + ( 10 - 1) * 0.16^2)/(12 + 10 -2)) = 0.134814688
SE = Pooled s * ((1/n1) + (1/n2)) = 0.134814687627128 * ((1/12) + (1/10)) = 0.057724201
t- score = 1.724718218
Width of the confidence interval = t * SE = 1.7247182182138 * 0.0577242005863514 = 0.09955798
Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = 0.190000000000001 - 0.0995579803831079 = 0.09044202
Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = 0.190000000000001 + 0.0995579803831079 = 0.28955798
The 90% confidence interval is [0.09, 0.29]
Since the confidence interval is entirely above 0, we can conclude that Machine 1 fills to more volume than Machine 2.
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