A fluorescent lamp manufacturer guarantees that the mean life of a fluorescent lamp is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of 32 fluorescent lamps. The results (in hours) are listed. Assume thepopulation standard deviation is 1850 hours. At a = 0.11, do you haveenough evidence to reject the manufacturer's claim?8,800 9,155 13,001 10,250 10,002 11,413 8,234 10,40210,016 8,015 6,110 11,005 11,555 9,254 6,991 12,00610,420 8,302 8,151 10,980 10,186 10,003 8,814 11,4456,277 8,632 7,265 10,584 9,397 11,987 7,556 10,380a) Write the claim mathematically and state the null and alternative hypotheses. b) Find the critical value(s) and identify the rejection region(s) for this test. Include a sketch of the rejection regions and explain how you would find the critical values using the standard normal distribution table.c) Find the standardized test statistic z, showing your work by hand using the formula. d) Based on your answers to parts b and c, decide whether to reject or fail to reject the null hypothesis based on the rejection regions. Explain your answer.e) Interpret the decision in the context of the original claim.