Please assist with question below regarding Quantitative Analysis and Decision Making.

A company that receives shipments of batteries tests a random sample of twenty-ve of them before agreeing to take a shipmem. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 40 hours. From past experience, it is safe to conclude that the population distribution of lifetimes is nomial with a standard deviation of 5 hours. For one particular shipment. the "lean lifetime for a sample or twenty-ve batteries was 38.8 hours. a. Test. at the 1% level. the null hypothesis that the population mean lifetime is at least 40 hours. I). Find the power are 1%|eve| test when the true mean lifetime of batteries Is 39 hours. B Cllck the Icon to vlew the standard normal dlstribution table, a. What are the null and allemeve hypotheses for this test? A. Hozp=40 .vo. Ho:pe4o H.:ps40 H1:p40 For thls test at the slgnlllcahee level a wlm sample mean it, hypotheslzed mean no, populetloh standard devlellon a, sample slze n, and z', or z\"l I 2, Vlrnel Is the term of the declsion rule? ;- \"o A- R ' ct H it > ale 0 o / Vn Z\" .vB . . ;' 'RejactHom:lu12 Determine the value for z\". zo. or :1\" , 2 as appropriate for this test. - 233 (Round to two decimal places as needed. Use a comma to separate answers as needed.) Calculate the test statistic. i _ 6 / n = 12 (Round to one decimal place as needed.) State the conclusion of this test. Do not reject the null hypothesis. There is nut suident evidence to conclude that the population mean lifetime is less than 40 hours. h. The power at this test when the true mean lifetime of batteries is 39 hours is (Round to four decimal places as needed.)