Question

A detergent manufacturer claims that the contents of boxes sold weigh on average 1
kg or more. It is known from historical records that the weights are normally distributed
with a standard deviation of 0.025 kg. A random sample of 16 boxes yielded a sample
mean weight of 0.987 kg. We are interested in whether the sample results show that
the manufacturer’s claim is invalid.
a) Do you recommend a hypothesis test with a one-sided alternative hypothesis or a
two-sided alternative hypothesis? Justify your answer.
b) Is the manufacturer’s claim invalid? Explain why or why not? Your answer should
be in the form of a hypothesis test at the 5% significance level.
c) Construct a 95% confidence interval for the average weight of the content of the
boxes.

Answer 1

(a) I recommend a hypothesis test with a one-sided alternative because the detergent manufacturer claims that the boxes weighed 1 kg or more. We will then check whether the boxes weighed less than 1 kg or not. We will be using a left-tailed hypothesis test for this.