Please help to solve these three MCQs.

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1. The Minister of Education of a country wants to study whether time spent in school (as measured by hours spent per day in school) leads to improved student performance (as measured by subject test scores). He wants to study this question because he wants to know if he should implement a longer school day. He is thinking of either having students spend 4 hours of their time each day in school, 6 hours, 8 hours, or 10 hours. He will pick the option which gives him the highest average student performance. Suppose he designs an experiment to answer this question. He randomly assigns students from a school at the start of the academic year to one of four groups. Group 1 spends 4 hours per day in school, Group 2 spends 6 hours per day in school, and so on. Each group contains more than 200 students. At the end of the academic year, he then administers a Math test to students in all 4 groups and computes the average test score for each of these groups, before picking the duration which produces the highest test score. Use the above information to answer questions 1 and 2. Which of the following statements is incorrect? (1 mark) If students who are initially assigned to attend only 4 hours of school each day secretly enrolled themselves for private tuition classes, then this will invalidate the results from the experiment. If some students who were initially assigned to attend 10 hours of school each day dropped out from this experiment because they leave the school for reasons unrelated to academic achievement (i.e. for random reasons) then the results of the experiment are still valid. If the test scores for those made to attend 10 hours of school per day are, on average, the highest, then the test scores for those made to attend 4 hours of school per day would be the lowest. The level of motivation of students in group 1 will be similar, on average, to the level of motivation of students in group 3. The average test score of students in group 4 (who spend 10 hours in school per day) reveal what the average test score of students in group 1 (who spend 4 hours in school per day) would have been if those in group 1 had been made to attend 10 hours of school per day. 2_ Suppose that the average test scores of students in group 1 are numerically different from the average test scores of students in group 4. Suppose, however, that the difference in the average test scores are not statistically significant, which of the following is correct? (1 mark) None of the options are correct. There is no evidence that the test scores of students made to attend 4 hours of school each day and the test scores of students made those made to attend 10 hours of school each day differ in the population. We can conclude that time spent in school has no effect on test scores. We can conclude that time spent in school affects test scores. This implies that the average test scores of students in group 2 will be numerically different from the average test scores of students in group 3. The President of a University wants to know if the class of honours a student obtains has any effect on his/her employment opportunities. In particular, he wants to know if employers have a preference for students who graduated with an honours with highest distinction vs students who graduated only with an honours with distinction. He visits the jobs classified section of the Straits Times and responds to the job advertisements in it. He creates 2 fictitious resumes which differ only in the applicant's class of honours and CAP but which are otherwise identical. He also includes a different photo on each of these 2 fictitious resumes. He then randomly sends these 2 resumes out to companies which list job advertisements, and records the number of times the highest distinction resume and the distinction resume receive an interview offer. The first resume is sent to 482 companies and the second resume is sent to 479 companies. He finds that the highest distinction resume receives a statistically significantly higher number of interview offers than the distinction resume. Which of the following is true? (1 mark) There is insufficient information to know whether receiving a highest distinction relative to a distinction boosts the likelihood of getting called up for an interview. The experiment does not reveal whether class of honours has any effect on his/her employment opportunities because the first resume was sent to 482 companies while the second resume was sent only to 479 companies. . Receiving a highest distinction relative to a distinction boosts the likelihood of getting called up for an interview. . The results from this experiment reveal the causal effect of class of honours on the probability of getting called up for an interview