Spring 2016 INEN 4320: Statistical Decision Making - Final Exam Name ___________________________________ L-Number ___________________ Signature ________________________________ By signing the honor pledge you are swearing that you have neither given nor received any unauthorized assistance before or during this examination. Any form of cheating will not be tolerated. 1. (15 points) A research measured the weight of 20 rats under experiment controls. Suppose there are 5 underweight rats. (a) Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. (8 points) (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02. (7 points) 2. (35 points) You have fit a multiple linear regression model and the ()1 matrix is: () 1 0.893758 0.0282448 0.0175641 = [ 0.028245 0.0013329 0.0001547 ] 0.0175641 0.0001547 0.0009108 (a) Please write the model of this multiple regression (2 points) (b) Assume the error sum of squares is 307, and there are 16 observations, what is the estimate of 2 (3 points) (c) Please calculate the standard error of the regression coefficients 1 and 2 (5 points). (d) Assume the estimated regression coefficients 1 and 2 are 2.74427 and 0.012528, respectively. Please calculate the 95% confidence interval for each of them (9 points). (e) Assume the intercept is 2.264, the two estimated regression coefficients are 2.74427 and 0.012528. Please construct a 95% prediction interval when x1=4 and x2= 250 (16 points). Page 1 of 2 3. (50 points) An engineering experiment was run with two factors, each factor run at high and low levels, as shown below. The observations were shown below. (a) Write a model for this experiment (5 points) (b) State the hypotheses of interest in this experiment (5 points) (c) Finish the ANOVA table. Please show all your calculations (35 points) (d) Draw your conclusions if alpha=5% (5 points). Experimental data High B Low B High A Low A 60 60 60 65 62 61 58 57 60 56 59 60 62 58 58 61 62 59 61 60 59 58 57 56 ANOVA Source of Variation A B SS Interaction AB Error Total 103.96 Note: Formulas needed to calculate SS: Page 2 of 2 df MS F P-value F crit / / /