3. Two machines are used for filling plastic bottles. Thel volume can be assumed
ID: 3311416 • Letter: 3
Question
3. Two machines are used for filling plastic bottles. Thel volume can be assumed nor- mal with standard deviation = 0.020 and 2 = 0.025 ounces. A member of the quality control staff suspects that both machinsl to the same mean net volumes. A random sample of 10 bottles is taken from each machines 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 16.0 15.96 16.02 16.01 16.01 15.99 16.00 (a) At significance level 0.05, do you think the engineer is correct? Use the rejection region approach. (b) Verify your conclusion of part (a) using the p-value approach (c) Find the 95% two sided confidence interval on the difference of the two means. Does this confidence interval verify your conclusion in part (a)?Explanation / Answer
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (10-1)*0.02^2+(10-1)*0.025^2/9+9
= 0.0005125
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(16.015-16.005)-0/0.0005125(1/10+1/10)
=0.01/0.01012423
=0.9877
tCRIT is +/-2.1 and hence computed value does not lie in the rejection region. Hence cannot reject the null hypothesis
The P-Value is .336391. The result is not significant at p < .05.
Confidence interval:-
(X1-X2)+-ta/2*Sp^2(1/n1+1/n2)
0.01+/-2.1*0.01
LCL=0.01-0.021=-0.011
UCL=0.01+0.021=0.031
(-0.011,0.031)
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