1. The Crown Bottling Company has installed a new bottling
process that will fill 12- ounce bottles of Cola. Both overfilling
and underfilling of bottles is undesirable. The company wishes to
see whether the mean bottle fill, µ, is approximately the target of
12 ounces. The standard deviation of the process is such that
σ=0.41. The company samples 32 bottles. Use a hypothesis test, at a
5% level of significance, and the sample mean to determine whether
the filler should be adjusted. The sample mean: 12.17
a) What is the null hypothesis and what is the alternative
hypothesis?
b) What is the rejection region? Show it in a picture and
explain.
c) What test statistic should you use? What is the value of
your test statistic?
d) What is your conclusion with respect to the null
hypothesis?
2. Now suppose the company is trying to cut costs and wants
to limit overfilling of bottles by more than 0.10 ounces. Use a
one-tailed hypothesis test to determine whether the mean is more
than 12.10 ounces. (Hint: follow all the steps outlined above)