Question 3 2 pts A large university wanted to study the relationship between completing an internship during college and students' future earning potential. Investigators selected a random sample of 80 students who completed an internship (X=1) and 100 students who did not complete an internship (X=0) and examined their salaries ve years after graduation (Y). They found that there was a statistically higher mean salary for the internship group than for the non-internship group. Select all of the following responses that are correct C] There could be a confounding variable, such as student major, that explains the difference in mean salary between the internship and no internship groups. C] We cannot infer anything from these data since the distribution of salaries is likely right skewed. C] You cannot draw any valid conclusions because the sample sizes are different. C] If the fitted regression equation is Y = a + bX, the value of b must be positive Question 4 2 pts When comparing among two or more fitted regression models, we always prefer the model with a higher coefficient of determination (R-squared). O True O FalseQuestion 5 2 pts Investigators are studying two anesthetics for individuals being treated for pain. The outcome is the time until complete numbing of pain (Y); two other variables are which anesthetic was given {X1=0 for drug A; X1=1 for drug B) and sex assigned at birth (X2=O for male; X2=1 for female). Select all of the following questions that are correct given the information in the table below. Estimate Std. Error t-valueQ-value (Intercept) 11.12 1.97 5.66 0.002 drug 2.59 3.03 0.85 0.395 sex 5.77 3.25 1.78 0.079 drug x sex -3.19 4.54 -0.70 0.485 R-squarecl 0.144 C] The p-value of 0.079 for sex tells us that there is no evidence of sex differences in mean time until numbing of pain. [3 The model with main effects only for drug and sex {no interaction) would have an R-squared value less than 0.144 C] The difference between the coefcients 5.77 and -3.19 tells us that sex is a confounder of the difference in mean time to numbing of pain between the two drugs. C] The p-value of 0.485 tells us that we have no evidence sex is an effect modifier of the difference in mean time to numbing of pain between the two drugs