Economic StatisticsECO 221Final ExamPlease, list your answers on separate word document and submit them viaBlackboard only!Suppose you produce coffee k cups. Last stage of production requires packing cups into boxes.Recently, your provider of machinery designed a new kind of machine that does packing fasterand with less damage than the machines he used to supply you with. To test the hypothesis thatnew machinery is indeed more productive, you receive a sample of ten new machines, then, youtake times it takes for each machine to pack 10 boxes. Here are the results for new machinescompared to the 10 old ones:New machinery, timein minutes 42.1 41 41.3 41.8 42.4 42.8 43.2 42.3 41.8 42.7Old machinery, timein minutes 42.7 43.6 43.8 43.3 42.5 43.5 43.1 41.7 44 44.11. The averages of packing time across two samples (1st– new machines, 2nd– old) are:a) Equalb) ?? ?=42.14, ?? ?=43.23c) ?? ?=42.99, ?? ?=43.23d) ?? ?=42.14, ?? ?=45.162. The standard deviation of packing time across two samples (1st– new machines, 2nd–old) are:a) Equalb) ? =0.145, ? =0.243c) ? =0.683, ? =0.243d) ? =0.683, ? =0.753. Are these two samples independent?a) Yesb) No4. The variances seem to be close enough across samples, so you consider equal populationvariance assumption. What kind of test will you proceed with?a) Pooled variance t-testb) Z-test5. You choose left tail test that difference between the two samples’ means is bigger orequal than zero, with ?=0.05. What is your pooled estimate of standard deviation?a) 0.818b) 0.717c) 0.919d) 0.2696. What is the calculated t-statistic for the test?a) -4.3b) -3.4c) -2.7d) -7.27. What is the rejection region for your hypothesis?a) t*