PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!! Measuring the actual dimensions of
ID: 3227111 • Letter: P
Question
PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!!
Measuring the actual dimensions of a manufactured part is a classical problem in many different disciplines, particularly for quality engineers. A quality engineer is measuring the thickness of nickel plates for use in a nickel-hydrogen battery. By the way the plate is made, she can consistently identify specific locations on each plate. That is, location A is in the same spot on each plate, and location B is in the same spot on each plate. She believes that measuring thickness at location A results in a consistently thicker measure than at location B. She measured thickness, in mm, at locations A and B on 10 particular plates. a. Conduct an appropriate hypothesis test with 95% confidence. Use the critical value approach. b. Produce a 99% confidence interval for the true mean difference in the thicknesses.Explanation / Answer
S.No Location A Location B Difference=A-B 1 31.10 29.75 1.35 2 31.10 29.75 1.35 3 30.90 30.15 0.75 4 30.80 30.80 0.00 5 32.20 30.20 2.00 6 30.40 30.40 0.00 7 29.65 30.35 -0.70 8 29.85 29.75 0.10 9 29.85 29.15 0.70 10 30.65 30.50 0.15 Mean of difference xbar 0.570 Standard deviation of Difference sd 0.815 Sample size n= 10 Degree of freedom df=n-1 9 Right Tailed 5% level critical t 1.833 Test statistic t=(xbar-0)/(sd/sqrt(n)) 2.213 We have to tets the null hypothesis H0: Mud=0 versus the alternative Ha: Mud>0 where Mud is the true mean of the difference in location A and B thickness. As calculated t>1.833, we reject the null hypothesis and conclude that the location A has higher mean than location B Two Tailed 1% level critical tc 3.250 99% Lower Limit=xbar-tc*sd/sqrt(n) 0.098 99% Upper Limit=xbar-tc*sd/sqrt(n) 1.042