(Q3): 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 o= 5% significance level. A random sample of 49 rivets from the lot purchased produces an average length of 3.015 cm. (a) Is this a 1-sided (i.e. a 1-tailed ) test ? Write down the Null and Alternate hypotheses. (b) Should the manager reject the null hypothesis ? Explain. (c) Unknown to the manager, the average rivet length is actually 3.04 cm. What is the manager's chance of committing a Type-2 error