A producer is very proud of the peaches he grows He claims t

A producer is very proud of the peaches he grows. He claims that, on average, 10% or less of his peaches in a bushel are defective. You take a sample of 400 peaches and find that 50 are defective. If = 0.025, what will be the decision?

Answer Choices:

a) Fail to reject the null; conclude that the defects are greater than 10%
b) Reject the null; conclude that the defects are not greater than 10%
c) Reject the null; conclude that the defects are greater than 10%
d) Fail to reject the null; conclude that the defects are not greater than 10%

Please show how to solve this question.

Solution

Set Up Hypothesis
Null, on average, 10% or less of his peaches in a bushel are defective H0:P<=0.1
Alternate, H1: P>0.1
Test Statistic
No. Of Success chances Observed (x)=50
Number of objects in a sample provided(n)=400
No. Of Success Rate ( P )= x/n = 0.125
Success Probability ( Po )=0.1
Failure Probability ( Qo) = 0.9
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.125-0.1/(Sqrt(0.09)/400)
Zo =1.6667
| Zo | =1.6667
Critical Value
The Value of |Z | at LOS 0.025% is 1.96
We got |Zo| =1.667 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.66667 ) = 0.04779
Hence Value of P0.025 < 0.04779,Here We Do not Reject Ho

We have evidence that on average, 10% or less of his peaches in a bushel are defective

ANS:
d) Fail to reject the null; conclude that the defects are not greater than 10%