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 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, S= 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 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 0.45.3. 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) State the conclusion (Reject Ho or Do not reject Ho) f. State the conclusion as a relationship to the