Problem 2 (15 points, 3 points for part 1, 2 points for each step of your test i
ID: 3181112 • Letter: P
Question
Problem 2 (15 points, 3 points for part 1, 2 points for each step of your test in part 2, and 2
points for part 3). Homes and Mergen (1992) studied a batch operation at a chemical plant where
an important quality characteristic was the product viscosity, which had a target value of 14.90.
Production personal use a viscosity measurement for each 12-batch to monitor this process. There
are the viscosities for the past ten batches.
13.3 14.5 15.3 15.3 14.3
14.8 15.2 14.9 14.6 14.1
(1) Find the sample mean and sample variance.
(2) Conduct a hypothesis test to see if the mean viscosity is changed. Use a significance level
of 0.05 and the rejection region approach for your test.
(3) Find the corresponding p-value for your test in part 2.
Explanation / Answer
(1) Sample Mean xbar=14.63 using excel function =AVERAGE(13.3,14.5,15.3,15.3,14.3,14.8,15.2,14.9,14.6,14.1)
Sample variance s2=0.39 using excel function =VAR(13.3,14.5,15.3,15.3,14.3,14.8,15.2,14.9,14.6,14.1)
Sample Stadard deviation s=sqrt(s2)=sqrt(0.39)=0.62
Sample Size n=10
(2) We are to test the null hypothesis H0: µ=14.90 versus the alternative H1:µ14.90
Test statistic t=(xbar-14.90)/(s/sqrt(n)) = (14.63-14.90)/(0.62/sqrt(10)) = -1.3771
Degree of freeom df=n-1=10-1=9
Two tailed Criticall value t(0.05/2,n-1)=t(0.05/2,9)=±2.2622 using excel funciton =TINV(0.05,9)
As Calculated |T|=1.3771<2.2622,, so we have not enoughe evidence to reject he null hypothesis and cocnldue that he mean viscosity has not changed.
(3) P-value=0.2018 using excel fucntion =TDIST(1.3771,9,2)