2. The XYZ Company manufactures woolen fabrics at several plants. The weekly production of the woolen fabrics follows a normal probability distribution, with a mean of 300 and a standard deviation of 15. Recently, due to market expansion, new production methods have been introduced and new employees hired. Over the last 50 weeks, the new methods have led to an average mean of 302 The vice president of manufacturing wants to know whether there has been an increase in the number of fabrics manufactured. can we conclude, because of the improved production methods, that the mean number of fabrics manufactured in the last 50 weeks was more than 300 at the 0.01 significance level? (10 marks)

a. State the Null and alternative hypotheses (2 marks)

b. What does the level of significance mean? (explain 2 marks)

c. What is the test statistic and why? (2 marks)

d. Formulate the decision rule (1 marks)

e. Make a decision and interpret the results (3 marks)