A production manager claims that the average production of h

A production manager claims that the average production of her employees is more than 30 an hour. A sample of 25 employees is taken; a mean of 33 and a standard deviation of 10 is found. Test at =0.025.

Solution

Set Up Hypothesis
Null, average production of her employees is less than 30 H0: U<30
Alternate, average production of her employees is more than 30 H1: U>30
Test Statistic
Population Mean(U)=30
Sample X(Mean)=33
Standard Deviation(S.D)=10
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =33-30/(10/Sqrt(24))
to =1.5
| to | =1.5
Critical Value
The Value of |t a| with n-1 = 24 d.f is 2.064
We got |to| =1.5 & | t a | =2.064
Make Decision
Hence Value of |to | < | t a | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.5 ) = 0.07333
Hence Value of P0.025 < 0.07333,Here We Do not Reject Ho

we have evidence that average production of her employees is less than 30