A maker of the microwave ovens advertises that less than 10

A maker of the microwave ovens advertises that less than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 57 microwaves that are 5 years old, 13% needed repairs. At alpha = 0.025, can you support the maker\'s claim? Round your answers to two decimal places.

Solution

Set Up Hypothesis
Null, H0:P<0.1
Alternate, H1: P>0.1
Test Statistic
Number of objects in a sample provided(n)=57
No. Of Success Rate ( P )= x/n = 0.13
Success Probability ( Po )=0.1
Failure Probability ( Qo) = 0.9
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.13-0.1/(Sqrt(0.09)/57)
Zo =0.755
| Zo | =0.755
Critical Value
The Value of |Z | at LOS 0.025% is 1.96
We got |Zo| =0.755 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 0.75498 ) = 0.22513
Hence Value of P0.025 < 0.22513,Here We Do not Reject Ho

We have evidence to support a marker of the micro ovens adevrtises that less than 10% of needs repair