Consider the following hypothesis test H0 mu GE 20 HA mu S

Consider the following hypothesis test: H0 : mu GE 20 HA : mu

Solution

Set Up Hypothesis
Null Hypothesis H0: U>=20
Alternate Hypothesis H1: U<20
Test Statistic
Population Mean(U)=20
Given That X(Mean)=19.4
Standard Deviation(S.D)=2
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=19.4-20/(2/Sqrt(50)
Zo =-2.1213
| Zo | =2.1213
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.1213 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -2.1213 ) = 0.0169
Hence Value of P0.05 > 0.0169, Here we Reject Ho

a)
Zo =-2.1213
b) ( P < -2.1213 ) = 0.0169
c) we Reject Ho
d) Reject Ho If Z<-1.64