(1o) Ii. (10) 1ii. (4) a) (4) b) Venn (2) C) Let p be the average fraction of \"grade A\" items produced by a certain company. In the past, p has been about 0.62. Of the remaining 38 percent, 3 percent were scrap and 35 percent were \"seconds.\" A new method is proposed that is expected to increase p. Under the new method, 250 items are produced, and 172 \"grade A\" items are found among them. Conduct a full hypothesis test to show that the new method has increased p. Leta = 0.05. In a study that contains a sample size of 100 teenagers, 23 of which work part time in the service industry, 26 teenagers work in retail, and 52 work part time in other sectors. Find the probability that a teenager works part time at only one of the two industry sectors listed above. (Draw a Venn diagram) Find the probability that a teenager works part time at both industry sectors listed above. (Draw a diagram) Are the two events mutually exclusive? Why or why not