A manufacturer of electronic instruments uses four assembly lines to produce the same instrument. Each assembly line is theoretically equivalent; hence all should have the same rate of production of instruments needing service under the warranty. The company wished to check this; therefore, a decision was made to look at the next 100 instruments returned to the factory as defective and determine how many came from each line. Now assebly line one is used for two work shifts per day, while assembly lines 2, 3, and 4 are each used for one shift per day. The defectives attributed to lines 1,2,3, and 4, respectively, are 53, 18, 14, and 15. Carry out the test for equivalence of the assembly lines using the 10% level of significance.
This is what I have done, and I was just wondering if it was done correctly.
Null Hypothesis: All of the lines are equally defective.
Alternative Hypothesis: All lines do not equally put out defective items.
Line 1=53
Line 2=18
Line 3=14
Line 4=15
{(53-40)^2}/40=4.225
{(18-20)^2}/20=.2
{(14-20)^2}/20=1.8
{(15-20)^2}/20=1.25
4.225+.2+1.8+1.25=7.475
DF=4-1=3@10%==6.25
The 7.475 is in the critical region, so you would reject the null and accept the alternative, is that correct? I am just trying to figure out if I am on the right path with these problems or not. Thank you.
This is what I have done, and I was just wondering if it was done correctly.
Null Hypothesis: All of the lines are equally defective.
Alternative Hypothesis: All lines do not equally put out defective items.
Line 1=53
Line 2=18
Line 3=14
Line 4=15
{(53-40)^2}/40=4.225
{(18-20)^2}/20=.2
{(14-20)^2}/20=1.8
{(15-20)^2}/20=1.25
4.225+.2+1.8+1.25=7.475
DF=4-1=3@10%==6.25
The 7.475 is in the critical region, so you would reject the null and accept the alternative, is that correct? I am just trying to figure out if I am on the right path with these problems or not. Thank you.