Consider the following hypotheses Which of the following sam

Consider the following hypotheses:

Which of the following sample information enables us to reject the null hypothesis at = 0.05 and at = 0.10? Use Table 1.

  (Click to select)RejectDo not reject

Solution

a)
x = 48; n = 100
No. Of Success chances Observed (x)=48
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.48
Success Probability ( Po )=0.54
Failure Probability ( Qo) = 0.46
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.48-0.54/(Sqrt(0.2484)/100)
Zo =-1.2
| Zo | =1.2
AT 0.05 LOS
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.204 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

AT 0.10 LOS
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =1.204 & | Z | =1.28
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

b)
Test Statistic
No. Of Success chances Observed (x)=141
Number of objects in a sample provided(n)=314
No. Of Success Rate ( P )= x/n = 0.45
Success Probability ( Po )=0.54
Failure Probability ( Qo) = 0.46
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.44904-0.54/(Sqrt(0.2484)/314)
Zo =-3.23
| Zo | =3.23

AT 0.05 LOS
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =3.234 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

AT 0.10 LOS
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =3.234 & | Z | =1.28
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

c)
Test Statistic
No. Of Success Rate ( P )= x/n = 0.47
Success Probability ( Po )=0.54
Failure Probability ( Qo) = 0.46
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.47-0.54/(Sqrt(0.2484)/64)
Zo =-1.12
| Zo | =1.12

AT 0.05 LOS
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.124 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

AT 0.10 LOS
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =1.124 & | Z | =1.28
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho

d)
Test Statistic
No. Of Success chances Observed (x)=198.81
Number of objects in a sample provided(n)=423
No. Of Success Rate ( P )= x/n = 0.47
Success Probability ( Po )=0.54
Failure Probability ( Qo) = 0.46
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.47-0.54/(Sqrt(0.2484)/423)
Zo =-2.89
| Zo | =2.89

AT 0.05 LOS
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.889 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

AT 0.10 LOS
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =2.889 & | Z | =1.28
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho