The Glen Valley Steel Company manufactures steel bars If the

The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with mean length of atleast 2.8 feet with a standard deviation of 0.20 foot (as determined from engineering specifications on the production equipment involved). Longer steel bars can be used or altered, but shorter bars must be scrapped. A sample of 25 bars is selected from the production line. The sample indicates a mean length of 2.73 feet. The company wants to determine whether the production equipment needs to be adjusted. State the null and alternative hypotheses. If the company wants to test the hypothesis at the 0.05 level of significance. what decision would be made using the critical value approach to hypothesis testing? If the company wants to test the hypothesis ai the 0.05 level of significance, what decision would be made using the p-value approach to hypothesis testing? Interpret the meaning of the p-value in this problem. Compare your conclusions in (b) and (c).

Solution

Set Up Hypothesis
Null, H0: U>=2.8
Alternate, H1: U<2.8
Test Statistic
Population Mean(U)=2.8
Given That X(Mean)=2.73
Standard Deviation(S.D)=0.2
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=2.73-2.8/(0.2/Sqrt(25)
Zo =-1.75
| Zo | =1.75
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.75 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -1.75 ) = 0.0401
Hence Value of P0.05 > 0.0401, Here we Reject Ho

It turns out steel bars with mean length are does n\'t follow
the rule atleast 2.8