4. Which of the following is the correct write-up for the interaction and (if significant) follow-up simple effects tests?

Between-Subjects Factors Value Label N Reward Condition (1 = No No Reward 60 Reward, 2 = Reward) Reward 60 Experimenter Gender (1 = Male 60 Male, 2 = Female) 2 Female 60 Descriptive Statistics Dependent Variable: Number of times the child helps Reward Condition (1 = No Experimenter Gender (1 = Reward, 2 = Reward) Male, 2 = Female) Mean Std. Deviation N No Reward Male 5.27 1.639 30 Female 7.10 2.339 30 Total 6.18 2.205 60 Reward Male 5.23 2.388 30 Female 5.40 1.522 30 Total 5.32 1.987 60 Total Male 5.25 2.030 60 Female 6.25 2.136 60 Total 5.75 2.135 120Tests of Between-Subjects Effects Dependent Variable: Number of times the child helps Type Ill Sum Source of Squares df Mean Square F Sig. Corrected Model 73.367 W 24.456 6.047 001 Intercept 3967.500 3967.500 981.022 000 RewardCondition 22.533 22.533 5.572 .020 GenderCondition 30.000 30.000 7.418 007 RewardCondition * 20.833 20.833 5.151 025 GenderCondition Error 469.133 116 4.044 Total 4510.000 120 Corrected Total 542.500 1194. Which of the following is the correct write-up forthe interaction and [if significant} follow-up simple effects tests? a. The interaction of Sincerity*lntentionality was significant, F{1,1ZCI} = 5.15, p c: .05. We would need to run four simple effects tests. 1}. We would look at the Sincere condition only [to see if the intentional and accidental conditions differed}. 2}. We would look at the insincere condition only (to see ifthe intentional and accidental conditions differed}. 3}. We would look at intentional condition only [to see if the sincere condition differed from the insincere condition}. 4}. We would look at the accidental condition only {to see ifthe sincere condition differed from the insincere condition}. b. The interaction of Sincerity*|ntentionality was significant was not significant, H1, 116} = 5.15, p 105. We would need to run four simple effects tests. 1}. We would look at the Sincere condition only {to see if the intentional and accidental conditions differed}. 2}. We would look at the insincere condition only {to see ifthe intentional and accidental conditions differed}. 3}. We would look at intentional condition onlyr [to see if the sincere condition differed from the insincere condition}. 4}. We would look at the accidental condition only {to see ifthe sincere condition differed from the insincere condition}. c. The interaction of Sincerity*|ntentionality was not significant, F{1,116}= 5.15, p >135. Since this is not significant, there was no need to run simple effects followup tests. d. The interaction of Sincerity*|ntentionality was significant. F{1,116}= 5.15, p -:: .05. We would need to run four simple effects tests. 1}. We would look at the Sincere condition only [to see if the intentional and accidental conditions differed}. 2}. We would look atthe insincere condition onlyr {to see ifthe intentional and accidental conditions differed}. 3}. We would look at intentional condition only [to see if the sincere condition differed from the insincere condition}. 4}. We would look at the accidental condition only {to see ifthe sincere condition differed from the insincere condition}. e. The interaction of Sinceritwlntentionality was not significant. H1. 120} = 5.15, p 105. Since this is not significant. there was no need to run simple effects followLip tests. Suppose we observe training data set of length N = 6: X = and y = The sample mean and the sample covariance matrix of class 0 and class 1 for training data are then XO = (3). So - (243 2) and x - (3) . s. = 3 (1 2) The (estimated) LDA rule then assigns x to class 1 if G(x) = Jo, BT (x - m) log(to/ 71) Note that above B =S '(X1 - XO) Xo + XI and m = 2 where S is the pooled SCM (i.e., S = ,So + ,S1, see lecture notes). In order to be fully manual, invert the 2 x 2 matrix using the rule (a b) ad - be ( " 25 ) (a) Calculate the rule G(x) and show all steps of your derivations. Use the empirical values for priors: To = No/N and m = M/N, where N = No + M is the number of observations in the training set, and N, is the number of observations in the ith class (i E {0, 1}). (b) Draw a scatter plot of the training data on a paper where you mark observations x with label y; = 0 by a circle (o) and with label y; = 1 with a square (0). Also plot the line AT (x - m) = log(To/#1), so the boundary of the classification regions. Also compute the training error rate.An oil well was drilled and discovered oil in an exploration prospect. The well tested 1 1 10 bbl/d oil of 23 .API. An oil sample was collected and PVT analysis revealed an oil formation volume factor of 1.15 rb/stb. Log analysis and geologic mapping resulted the following average reservoir properties: Drainage area = 813 acres Net pay thickness = 77 ft Porosity = 0.21 Water saturation = 0.27 1. Calculate the mid case oil resources using a deterministic approach (volumetric equation below). 7758Aho(1 -5_) 4758 ( 813)(77) (0:21) (1-0:27) = 64 . 74 X10 S TB STOUP = 1.75 2. Build a Monte Carol Simulation in Excel using the following input parameters and develop a cumulative distribution curve and probability distribution curve for the resources. Parameter Distribution Type Statistical Parameters Hint: XLS Function to be used Area NORMAL Mean: 813 acres NORM.INV Std. Dev: 0.2 Thickness LOGNORMAL Mean: 77 ft LOGNORM INV Sid Dev: 0.15 Porosity NORMAL Mean: 0.21 NORM.INV Std. Dev: 0.028 Oil Saturation BETA Alpha : 0.16 BETA INV Beta : 0.07 lower bound: 0.31 upper bound: 0.83 Oil FVF Constant 1.15 rb/stb Recovery Factor | LOGNORMAL Mean: 23% LOGNORM INV St. Dev.: 6 25% 3. Estimate P10, P50 and P90 resources. 4. Compare mean resources estimated using deterministic approach and probabilistic approach and explain reason(s) for major variance, if any.Hints on building Monte Carlo Simulation in XLS: A - Do the following 1. Select cell G4 and type in "Iteration". 2. Select cell G5 and type in 1. Go to to fill out 2000 iteration numbers in column A. Select , an increment of I and a stopping value of 2000. Click . 3. Type input parameters names in cells H4:M4 4. Type the appropriate distribution type of each parameters in the row above (H3:M3) 5. Use appropriate XLS function for each property to distribute random parameters (e.g. for Area type =LOGNORM. INV(RAND(),LN(790),0.19) in cell H5) 6. Perform 2000 iterations for each of the properties by select cells H5 and holding down the key and select cell M2004. Press the key combination which will copy the content of cells H5:M5 down through cells H2004:M2004.\f