14 Math Methods for Mechanical Engineers (22.3610) For\teach\tof\tthe\tfollowing\tproblems,\tperform\ta\thypothesis\ttest\tshowing\tall\t4\tsteps\tof\tthe process,\tthen\tanswer\tHW14\tquestions\ton\tBlackboard, a. Suppose\ta\tproduction\tline\toperates\twith\ta\tmean\tfilling\tweight\tof\t16\tounces\tper\tcontainer. Since\tover-\tor\tunder-filling\tcan\tbe\tdangerous,\ta\tquality\tcontrol\tinspector\tsamples\t40\titems to\tdetermine\twhether\tor\tnot\tthe\tfilling\tweight\thas\tto\tbe\tadjusted. The\tsample\trevealed\ta mean\tof\t16.32\tounces. From\tpast\tdata,\tthe\tstandard\tdeviation\tis\tknown\tto\tbe\t.8\tounces. Using\ta\t0.05\tlevel\tof\tsignificance,\tcan\tit\tbe\tconcluded\tthat\tthe\tprocess\tis\tout\tof\tcontrol\t(not equal\tto\t16\tounces)? b. An\teditor\tof\ta\tpublishing\tcompany\tclaims\tthat\tthe\tmean\ttime\tto\twrite\ta\ttextbook\tis\tat\tmost 15\tmonths. A\tsample\tof\t25\ttextbook\tauthors\tis\trandomly\tselected\tand\tit\tis\tfound\tthat\tthe mean time taken by them to write a textbook was 12.5 months. Assume also that the standard deviation is known to be 5 months. Assuming the time to write a textbook is normally distributed and using a 0.025 level of significance, would you conclude the editor's\tclaim\tis\ttrue? c. According\tto\ta\t1990\tdemographic\treport,\tthe\taverage\tU.\tS.\thousehold\tspends\t$90\tper\tday. Suppose you recently took a random sample of 30 households in Lowell and the results revealed\ta\tmean\tof\t$94.50. Suppose\tthe\tstandard\tdeviation\tis\tknown\tto\tbe\t$15.50. Using\ta 0.05\tlevel\tof\tsignificance,\tcan\tit\tbe\tconcluded\tthat\tthe\taverage\tamount\tspent\tper\tday\tby\tU.S. households\thas\tincreased