3. An experiment was conducted where paper brightness (measured by a reflectance meter) was recorded for paper samples produced using 4 different settings (a,b,c,d). The data are in the file "paper.txt" posted on canvas. (a) (6 points) Is there statistical evidence, at the 1% significance level, that the predictor operator is significant in the linear regression model with response bright? Perform the appropriate hypothesis test and state the assumptions that you are making about the data. (b) (3 points) Use AIC and BIC to select between the model with the predictor operator and the model with no predictors (the intercept-only model). How do these selections compare to the hypothesis test result in part 3a ?

paper.txt:

"bright" "operator" "1" 59.8 "a" "2" 60 "a" "3" 60.8 "a" "4" 60.8 "a" "5" 59.8 "a" "6" 59.8 "b" "7" 60.2 "b" "8" 60.4 "b" "9" 59.9 "b" "10" 60 "b" "11" 60.7 "c" "12" 60.7 "c" "13" 60.5 "c" "14" 60.9 "c" "15" 60.3 "c" "16" 61 "d" "17" 60.8 "d" "18" 60.6 "d" "19" 60.5 "d" "20" 60.5 "d"