BT2101 Problemset 1: Hypothesis Testing This problem-set is due on 'Ihe 23 Aug 2022 by 23:59 1 Problem 1: Automatic Robots A factory has just purchased a new robot to automate the task of placing items onto packing shelves. The manufacturer claims that the robot can place items with an error less than 0.3cm. You collect a large sample of observations on the new robot's placement. With your training in statistics, you are asked to help the factory manager test the manufacturer's claim. Answer the following questions: (a) Please state your null and alternative hypothesis (b) How does the p-value of your sample mean change as you decrease the signicance level of your hypothesis test? (c) How does the outcome of your hypothesis test change as you decrease the signicance level of your hypothesis test? 2 Problem 2: Gender Wage Differences To investigate possible gender discrimination in a large rm {called Doogle), male and female employees were selected at random and their salary information was collected. Suppose the average monthly salary of male employees is #M: and the average monthly salary of female employees is up Answer the following questions: (a) State the null and alternative hypotheses to be used for the investigation. Remember that we presume there is no gender discrimination in Dougie until proven otherwise. (b) Would you consider running a one-tailed or two-tailed test? Explain briey. (c) Now we choose 10 men and 10 women from one department. The sample mean of men is $6000, whereas the sample mean of female is $5000. Can we conclude that Doogle is guilty of gender discrimination in its compensation policies? Please support your stand with justication. 3 Problem 3: Weight of Apple Pies Recently, there have been complaints about a local bakery that the baker does not put the advertised amount of apples in the apple pies The bakery advertises that each apple pie contains at least 500g of apples. Answer the following questions: (a) Formulate the appropriate null and alternative hypotheses Remember that the bakery is presumed to be innocent until proven guilty. (b) Would you consider running a one-tailed or two-tailed test? Explain how it is related to the notion of the bakery being innocent until proven guilty. (c) Theory suggests that \" Even though you rejected the null hypothesis, it may still be true.\" \"That can you do to protect yourself from making such a mistake rejecting the null hypothesis, while it is true