A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 435.0435.0 gram setting. It is believed that the machine is underfilling the bags. A 4646 bag sample had a mean of 429.0429.0 grams. A level of significance of 0.050.05 will be used. Determine the decision rule. Assume the standard deviation is known to be 24.024.0.

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, = 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

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

Formula:

Putting all the values, we have

Now,

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,

We reject the null hypothesis and accept the alternate hypothesis. Thus,  the machine is underfilling the bags.