A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 36 containers whose packaging states that the contents weight 8 ounces was drawn. The contents were weighed and the results are shown below.

a. Identify the null and alternative hypotheses used to determine whether the mean weight of the contents is less than that advertised on the package. (Express symbolically if possible.)

b. Conduct a hypothesis test using = 0.01. Show and label the calculations for the hypothesis test below:

c. State and justify the conclusions based on the results of the hypothesis test.

Weights 7.80 7.91 7.93 7.99 7.94 7.75 7.97 7.95 7.79 8.06 7.82 7.89 7.92 7.87 7.92 7.98 8.05 7.91 7.80 7.91 7.93 7.99 7.94 7.75 7.97 7.95 7.79 8.06 7.82 7.89 7.92 7.87 7.92 7.98 8.05 7.91