Answer:
The calculated value z= 0.0063 does not fall in the critical region so we fail to reject the null hypothesis. And accept that the valve does not perform above the specifications.
Step-by-step explanation:
Given that
Population mean= μ = 8.0
Sample mean= x`= 8.1
Sample size= n= 250
Sample standard deviation= s= 1.00
Significance level= ∝ =0.01
The null hypothesis and alternate hypothesis are
H0: μ < 8.0
Ha: μ ≥ 8.0 One tailed test
The claim is that the valve perform above the specifications
The critical value at 0.01 significance level for one tailed test is z > ±2.33
The test statistic z is used
z= x`- μ/ σ/√n
Z= 8.1-8.0/ 1/√250
z= 0.1/1/15.811
z= 0.0063
The calculated value z= 0.0063 does not fall in the critical region so we fail to reject the null hypothesis.
