3. The quality control manager at a light bulb factory needs to determine whether the average life of a large shipment of light bulbs is equal to the specified value of 475 hours. The process standard deviation is known to be 200 hours. A random sample of 49 light bulbs indicates a sample mean life of 470 hours. At the 0.05 level of significance, is there evidence that the mean life is less than 475 hours? [10 points] a. State the null and alternative hypothesis b. Is it a two-tail test or one-tail test? c. Write the test Statistic (Z or T)? d. State the critical value(s) e. State the conclusion (Reject Ho or Do not reject Ho) f. State the conclusion as a relationship to the problem.1. The personnel director of a large corporation wants to study absenteeism among clerical workers at the corporation's central office during the year. A random sample of 35 clerical workers reveals the following: [10 points] Absenteeism: X = 19.7 days, $= 5.0 days. 15 clerical workers were absent more than 12 days. a. Set up an 80 % confidence interval estimate of the average number of absences for clerical workers last year. b. Set up a 92% confidence interval estimate of the population proportion of clerical workers absent more than 12 dayslast year. c. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 85% confident of being correct to within + 1.5 days and the population standard deviation is assumed to be 4.5 days? d. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 90% confident of being correct to within 1 0.075 of the population proportion of workers who are absent more than 12 days if the population proportion is known to be 0.45.2. The quality control manager at a light bulb factory needs to determine whether the average life of a large shipment of light bulbs is equal to the specified value of 475 hours. The process standard deviation is known to be 200 hours. A random sample of 36 light bulbs indicates a sample mean life of 480 hours. At the 0.10 level of significance, is there evidence that the mean life is different from 475 hours? [10 points] a. State the null and alternative hypothesis b. Is it a two-tail test or one-tail test? c. Write the test Statistic (Z or T)? d. State the critical value(s) e. State the conclusion (Reject Ho or Do not reject Ho) f. State the conclusion as a relationship to the