Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 408 grams with a standard deviation of 14. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

The decision rule for rejecting the null hypothesis is
`t < -1.721`

Explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:

`H_0: \mu = 410`

At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:

`H_0: \mu < 410`

Type of test:

As we test if the mean is less than a value, we have a left-tailed test.

We have the standard deviation for the sample, which means that the t-distribution is used.

We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.

Using a calculator, the critical value is
`t_c = -1.721`

Determine the decision rule for rejecting the null hypothesis.

We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is
`t < -1.721`