Respuesta :
Answer:
The machine is underfilling the bags.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 435.0 grams
Sample mean, [tex]\bar{x}[/tex] = 429.0 grams
Sample size, n = 46
Alpha, α = 0.05
Population standard deviation, σ = 24.0 grams
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 435.0\text{ grams}\\H_A: \mu < 435.0\text{ grams}[/tex]
We use one-tailed 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{429.0 - 435.0}{\frac{24.0}{\sqrt{46}} } = -1.695[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -1.64[/tex]
Decision Rule:
If the calculated z statistic is less than the critical value of z, we fail to accept the null hypothesis and reject it.
Since,
[tex]z_{stat} < z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis. Thus, the machine is underfilling the bags.
