Answer:
We conclude that the bag filling machine works correctly at the 444.0 gram setting.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 444.0 gram
Sample mean, [tex]\bar{x}[/tex] = 443.0 grams
Sample size, n = 40
Alpha, α = 0.02
Population standard deviation, σ = 23.0 grams
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 444.0\text{ grams}\\H_A: \mu < 444.0\text{ grams}[/tex]
We use one-tailed(left) 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{443 - 444}{\frac{23}{\sqrt{40}} } =-0.274[/tex]
Now, [tex]z_{critical} \text{ at 0.02 level of significance } = -2.054[/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 bag filling machine works correctly at the 444.0 gram setting.
