Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444.0 gram setting. it is believed that the machine is underfilling the bags. a 40 bag sample had a mean of 443.0 grams. a level of significance of 0.02 will be used. determine the decision rule. assume the standard deviation is known to be 23.0.

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, = 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

We use one-tailed(left) z test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,  

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.