Please answer a and b Consider the following hypothesis test

Please answer a and b

Consider the following hypothesis test A sample Of 50 provide a sample of 9.46 and sample standard derivation of 2.

Solution

Set Up Hypothesis
Null, H0: U=10
Alternate, H1: U<10
Test Statistic
Population Mean(U)=10
Sample X(Mean)=9.46
Standard Deviation(S.D)=2
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =9.46-10/(2/Sqrt(50))
to =-1.909
| to | =1.909
Critical Value
The Value of |t | with n-1 = 49 d.f is 1.677
We got |to| =1.909 & | t | =1.677
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -1.9092 ) = 0.03105
Hence Value of P0.05 > 0.03105,Here we Reject Ho

[ANSWERS]
a.
Critical Value, t with n-1 = 49 d.f is -1.677, Reject Ho if to<-1.677
b.
to =-1.909