Question

A company that packages salted peanuts in 12-ounce jars is interested in checking how well one of its machines is functioning. Proper functioning would mean averaging 12 ounces of peanuts per jar and not consistently over or under-filling the jars. To test the machine, a sample of 100 jars is taken from the line at random time intervals and their contents weighted. The sample mean weight of a jar turns out to be 12.5 ounces. Using a significance level of α = 0:05, please check if an adjustment is necessary for the machine filling the jars. Explicitly state your hypothesis, go through all steps and make sure you make a recommendation at the end. Conduct the hypothesis test assuming that σ 2 is known to be equal to 6:4. Perform the hypothesis test by:

a) looking at the observed value vs the critical value.

b) computing the p-value and comparing it to α = 0:05.

c) constructing a 95% confidence interval. Make sure you write the hypotheses tests and the test statistic.

Answer 1

Let denotes the true average weight of a jar.

c)