Statistic and probability?

Question

A potato chip company packages its potato chips into 12.0 ounce bags. You find it hard to believe that the bag contains enough potato chips to weigh 12.0 ounces and would like to make an official complaint. Before doing so, you decide to run an experiment so that you can have some confidence that the company’s claim is incorrect. Over the next several months you buy 30 bags of potato chips and weigh the contents of each one. You discover that the mean weight is 11.9 ounces with a standard deviation of 0.4 ounces. You decide that you will only complain if you can be 95% sure that the bags do not contain at least 12.0 ounces of potato chips. You decide to construct a hypothesis test.
Using a standard table, you determine that the critical value is –1.645. Determine if you are able to reject the null hypothesis and explain how you reached this conclusion. (Your conclusion should include a comment relating the results to the original problem.)

which average is being considered. Do these hypotheses apply to the sample mean or the population mean? Please, clarify.

Answer 1

First of all, you state your null hypothesis. H0: mean is >= 12.0 ounces. The alternative hypothesis is H1: mean is < 12.0 ounces. Note that this is a one-tailed test; you don't care if there are more than 12 ounces on average.

Using the z distribution with critical value = -1.645, if calculated z < critical z, then reject H0 in favor of H1.

z (calculated) = (11.9 - 12.0) / (0.4 * sqrt(30)) = -0.0456.

Fail to reject H0, cannot conclude that bags are systematically under-filled.

(You'd actually want to use the t distribution rather than the z-distribution you appear to mention (with critical value = 1.645), because you do not know the population standard deviation. You still won't reject your null.)