Question

A manufacturer 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.

Answer 1

We conclude that the bag filling machine works correctly at the 444.0 gram setting.

Explanation:

We are given the following in the question:

Population mean, μ = 444.0 gram

Sample mean,
`\bar{x}` = 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

`H_(0): \mu = 444.0\text{ grams}\\H_A: \mu < 444.0\text{ grams}`

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

Formula:

`z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

Putting all the values, we have

`z_(stat) = \displaystyle(443 - 444)/((23)/(√(40)) ) =-0.274`

Now,
`z_(critical) \text{ at 0.02 level of significance } = -2.054`

Since,

`z_(stat) < z_(critical)`

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.