About.8% of the items produced on an assembly line are detective and must be dis
ID: 3152842 • Letter: A
Question
About.8% of the items produced on an assembly line are detective and must be discarded. A supervisor is concerned the fraction of defective items may be larger. A sample of 400 items reveals that 9 of them are defective. Test to see if the fraction of defective items has increased. Use a 5% level of significance. Long term sales records of a product show that sales of five varieties occur in a 3: 2: 2: 1: 1 ratio. The number of items of each variety sold in the last month are 297, 193, 164, 86, and 80 respectively. Test to see it the jiven distribution still holds at a 5% level of significance.Explanation / Answer
Q7.
Set Up Hypothesis
Null,defective item is increased H0:P>0.08
Alternate, H1: P<0.08
Test Statistic
No. Of Success chances Observed (x)=9
Number of objects in a sample provided(n)=400
No. Of Success Rate ( P )= x/n = 0.0225
Success Probability ( Po )=0.08
Failure Probability ( Qo) = 0.92
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.0225-0.08/(Sqrt(0.0736)/400)
Zo =-4.239
| Zo | =4.239
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =4.239 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -4.23896 ) = 0.00001
Hence Value of P0.05 > 0.00001,Here we Reject Ho
We have evidence that the fracction of defective items has increased