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 thatthe manufacturer's claim is invalid.

1. a)Do you recommend a hypothesis test with a one-sided alternative hypothesis or a two-sided alternative hypothesis? Justify your answer.
2. b)Is themanufacturer'sclaim invalid? Explain why or why not? Your answer should be in the form of a hypothesis test at the 5% significance level.
3. c)Construct a 95% confidence interval for the average weight of the content of the boxes.