Direction: Solve the following problems in the space provided. (71 - 12) - do 2 = (1 - 12 do o1 and o2 known #1 - 12 7 do 2 2Q/2 A random sample of size n, = 25, taken from a normal population with a Two kinds of thread are being compared for strength. Fifty pieces of each type standard deviation of = 5, has a mean x1 = 80. A second random sample of thread are tested under similar conditions. Brand A has an average tensile of size n2 = 36, taken from a different normal population with a standard strength of 78.3 kilograms with a standard deviation of 5.6 kilograms, while brand deviation oz = 3, has a mean xz = 75. Using 5% level of significance, B has an average tensile strength of 87.2 kilograms with a standard deviation of check whether #1 > H2 6.3 kilograms. Using a=0.01, test the hypothesis that the mean strength of brand B has a higher strength than that of Brand A. Reject Ho: (1 > H2 Reject Ho: HB > HA 1 = - (51 - 12) - do MpVI/m + 1/12 "= m1 + n2 - 2. #1 - 12 do 1> to 1 - 12 4 do t ta/2 "1 + 12 - 2 The following data represent the length of time, in days, to recovery for patients An experiment reported in Popular Science compared fuel economies for two randomly treated with one of two medications to clear up severe bladder types of similarly equipped diesel mini-trucks. Let us suppose that 12 infections: Volkswagen and 10 Toyota trucks were tested in 90- kilometer-per-hour steady- Medication 1 Medication 2 paced trials. If the 12 Volkswagen trucks averaged 16 kilometers per liter with a 16 standard deviation of 1.0 kilometer per liter and the 10 Toyota trucks averaged 17 19 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter, Using 1.5 1.8 0.05 level of significance, determine if the mean if the fuel economy of for the Using 0.01 level of significance, determine if medication 1 is more effective in average kilometers per liter for these two mini-trucks are equal. Assume that the treating the infection than medication 2, assuming normal populations with distances per liter for the truck models are approximately normally distributed equal variances with equal variances. The fuel economy of for the average kilometers per liter for these two mini-trucks Reject Ho: Medication 1 is more effective than Medication 2. are different