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Scores before Training 41 35 37 46 53 38 44 40 43 Scores after Training 47 28 26 54 42 17 44 31 44 a) Has any change taken place? Test your claim at 5% level. (3) h) Obtain 95% confidence interval for the mean change in ability of trainees (4) " Compute Pearson's comelation coefficient between the scores before and after training and test its significance using t-test at 5% level of significance. 161 [13] The following measurements, Air velocity (cm/secs) and Evaporation coefficients (mm /secs) of burning fuel droplets in an impulse engine. Air Velocity: x 20 60 100 140 180 220 260 300 340 380 Evaporation Coefficient y 0.18 0.37 0.35 0.78 0.56 0.75 1.18 1.36 1.17 1.65 For the above data, a regression model y = o+ + is to he fitted a) State the assumptions on this model. (1) bi Obtain the least squares estimate of a and 141 c) Compute an unbiased estimate of the error variance (2) di Obtain 95% confidence interval for a (21 e) Test the hypothesis ( - 0 against /=0 at 5% level (31 1 95% confidence interval for evaporation coefficient when air velocity is 190 en /sec [141 A fire insurance company intending to alter its logo. sent questionnaires to a sample of its employees asking their opinions about three possibilities. The employees were asked to award each of the three logos (A,B and C), a score out of five on six different aspects of design, color and so on. The total scores awarded by the eight employees are given below. Employees 2 3 5 6 7 Lugus A 22 19 14 18 21 18 23 20 24 21 15 20 21 21 18 19 15 16 19 18 15 10 18 Test the hypothesis that the dree logos are equally preferred by the employer, al 3% level of significance. [6] Suppose (X. Y) have joint pdf f(x,y)- 2expi (x ly)|; Ogyex