(Q2): A manager of a construction company has purchased a large lot of steel rivets that are supposed to average 3 cm in length, with a standard devi- ation of 0.07 cm. However, she suspects that the average rivet length in the lot she purchased is not 3 cm.The manager conducts a hypothesis test at the a= 5% significance level. A random sample of 49 rivets from the lot purchased produces an average length of 3.035 cm. a) Construct a 95% (= 1 - a) confidence interval for the average rivet length. b) Should the manager reject the null hypothesis? c) Unknown to the manager, the average rivet length is actually 3.03 cm. What is the manager's chance of committing a Type 2 error