Answer:
We conclude that the mean strength is equal to 3400 psi.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 3400 psi
Sample mean, [tex]\bar{x}[/tex] = 3450 psi
Sample size, n = 12
Alpha, α = 0.051
Population standard deviation, σ =75 psi
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 3400\text{ psi}\\H_A: \mu > 3400\text{ psi}[/tex]
We use one-tailed(right) z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{3450 - 3400}{\frac{75}{\sqrt{12}} } = 2.309[/tex]
Now,
[tex]z_{critical} \text{ at 0.05 level of significance } = 2.33[/tex]
Since,
[tex]z_{stat} < z_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that the mean strength is equal to 3400 psi.
