I'= _ (51 - 52) - do Vailm + $5y 141 - 12 do 1'> to #1 - 12 * do t' ta/2 01 # 02 and unknown The following data represent the running times of films produced by two A study was conducted by the Department of Zoology at the Virginia Tech to motion-picture companies. estimate the difference in the amounts of the chemical orthophosphorus Company Time (minutes) measured at two different stations on the James River. Orthophosphorus was 103 94 110 87 98 measured in milligrams per liter. Fifteen samples were collected from station 1, 97 82 123 92 175 88 118 and 12 samples were obtained from station 2. The 15 samples from station 1 Test the hypothesis that My = My against u, * My using 0.01 level of had an average orthophosphorus content of 3.84 milligrams per liter and a significance. Assume that the running-time differences are approximately standard deviation of 3.07 milligrams per liter, while the 12 samples from station normally distributed with unequal variances. 2 had an average content of 1.49 milligrams per liter and a standard deviation of 0.80 milligram per liter. Test the hypothesis that true average orthophosphorus contents at these two stations are equal using 0.02 level of significance, assuming that the observations came from normal populations with different variances. The mean running time is the same. The average orthophosphorus contents at these two stations are different. up = do 1 = - d - do. paired up > do > to observations up # do t to/2 The federal government awarded grants to the agricultural departments of 9 | Fortune magazine (March 1997) reported the total returns to investors for the 10 universities to test the yield capabilities of two new varieties of wheat. Each years prior to 1996 and also for 1996 for 431 companies. The total returns for 10 variety was planted on a plot of equal area at each university, and the yields, in of the companies are listed below. Using 0.05 level of significance, test the kilograms per plot, were recorded as follows: difference between mean change in percent return to investors. University Total Return to Investors Variety 1 2 3 4 5 6 7 8 9 Company 1986-96 1996 38 23 35 41 44 29 37 31 38 Coca-Cola 29 8% 13.3% 45 25 31 38 50 Mirage Resorts 27.9% Merck 22.1% 2 1.0% Using 0.05 level of significance, determine if there is a significant difference Microsoft 41.5% 88.3% Johnson & Johnson 22.2% 18.1% between the yields of the two varieties, assuming the differences of yields to be Intel 13.8% 131.2% approximately normally distributed. Explain why pairing is necessary in this Pfizer 21.7% 340% Procter & Gamble 21.1% 32.1% problem. Berkshire Hathaway 28.30 6.2% S&-P 500 11.8% 20.3% No significant difference between brand 1 and brand 2. There is no significant difference between the net change of percentage return