#1 #₂ = do I Company Time (minutes) 87 110 123 92 (1-2₂)-do √3²/12₁ +23/1₂ (7/1₁+1₂)² (0/0)² + (0//m₂) 11-1 00₂ and unknown The following data represent the running times of films produced by two motion-picture companies. t' = t= 103 94 97 82 88 118 Test the hypothesis that against , using 0.01 level of significance. Assume that the running-time differences are approximately normally distributed with unequal variances. 98 175 No significant difference between brand 1 and brand 2. 2-do $4/√ University 1 2 3 4 5 6 7 89 38 23 35 41 44 29 37 31 38 45 25 31 38 50 33 36 40 43 The mean running time is the same. The average orthophosphorus contents at these two stations are different. PD = do paired observations #D do PD do t<-fa/2 or 1>fa/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. Total Return to Investors 1986-96 1996 Variety Using 0.05 level of significance, determine if there is a significant difference between the yields of the two varieties, assuming the differences of yields to be approximately normally distributed. Explain why pairing is necessary in this problem. P1-P₂ do P1-P2 # do t> to t'<-to/2 or f> to/2 A study was conducted by the Department of Zoology at the Virginia Tech to estimate the difference in the amounts of the chemical orthophosphorus measured at two different stations on the James River. Orthophosphorus was measured in milligrams per liter. Fifteen samples were collected from station 1, and 12 samples were obtained from station 2. The 15 samples from station 1 had an average orthophosphorus content of 3.84 milligrams per liter and a standard deviation of 3.07 milligrams per liter, while the 12 samples from station 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. t<-lo t>fa Company Coca-Cola Mirage Resorts Merck Microsoft Johnson & Johnson 29.8% 27.9% 22.1% 44.5% 22.2% 43.8% Intel Pfizer 21.7% 21.9% Procter & Gamble Berkshire Hathaway 28.3% S&P 500 43.3% 25.4% 24.0% 88.3% 18.1% 131.2% 34.0% 32.1% 6.2% 20.3% There is no significant difference between the net change of percentage returns