A manufacturer of machine rods produces units a rod diameter

A manufacturer of machine rods produces units a rod diameter that can be regarded as a random variable.  The variance of the rods produces is known and is found to be 0.25 mm².

A sample of 37 rods is taken from production line 3 is found to have an average of 13.532 mm.  Does this data support the foreman

Solution

Set Up Hypothesis
Null Hypothesis H0: U<13.4
Alternate Hypothesis H1: U>13.4
Test Statistic
Population Mean(U)=13.4
Given That X(Mean)=13.532
Standard Deviation(S.D)=0.5
Number (n)=37
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=13.532-13.4/(0.5/Sqrt(37)
Zo =1.6058
| Zo | =1.6058
Critical Value
The Value of |Z ?| at LOS 0.05% is 1.64
We got |Zo| =1.6058 & | Z ? | =1.64
Make Decision
Hence Value of |Zo | < | Z ? | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.6058 ) = 0.0542
Hence Value of P0.05 < 0.0542, Here We Do not Reject Ho