Company A makes a large shipment to Company B Company B can

Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of defective items in the shipment is larger than 0.1. In a sample of 400 items from the shipment, Company B finds that 53 are defective. Conduct the appropriate hypothesis test for Company B using a 0.1 level of significance.

a) What are the appropriate hypotheses?

H₀: p = 0.1 versus H_a: p 0.1H₀: p = 0.1 versus H_a: p > 0.1    H₀: p = 0.1 versus H_a: p < 0.1H₀: = 0.1 versus H_a: > 0.1

b) What is the test statistic? Give your answer to four decimal places.  

c) What is the critical point for the test? Give your answer to four decimal places.  

d) What is the appropriate conclusion?

Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point.Fail to reject the claim that the defective proportion in the shipment is 0.1 because the test statistic is smaller than the critical point.    Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is smaller than the critical point.Fail to reject the claim that the defective proportion in the shipment is 0.1 because the test statistic is larger than the critical point.

Solution

Set Up Hypothesis
Null,proportion of defective items has no change in defective H0:P=0.1
Alternate, proportion of defective items in the shipment is larger than 0.1 H1: P>0.1
Test Statistic
No. Of Success chances Observed (x)=53
Number of objects in a sample provided(n)=400
No. Of Success Rate ( P )= x/n = 0.1325
Success Probability ( Po )=0.1
Failure Probability ( Qo) = 0.9
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.1325-0.1/(Sqrt(0.09)/400)
Zo =2.1667
| Zo | =2.1667
Critical Value
The Value of |Z a| at LOS 0.1% is 1.28
We got |Zo| =2.167 & | Z a | =1.28
Make Decision
Hence Value of | Zo | > | Z a| and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.16667 ) = 0.01513
Hence Value of P0.1 > 0.01513,Here we Reject Ho

ANS: H0: p = 0.1 versus Ha: p > 0.1, Zo =2.1667, at LOS 0.1% is 1.28,
Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point