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# Over the last three years, Dr.

Over the last three years, Dr. Farrell has asked students in the Fall online section of STAT 2606 to participate in a poll to help him choose a Halloween costume. He posted the poll on cuLearn, and had students participate on a voluntary basis. The same three choices were given each year, always in the following order: Construction Barrel, Minion, and Baseball Player (If you wish to see pictures, open the pdf file just below the file containing the assignment). Dr. Farrell asked the students to rank the costumes from most favoured to least favoured with scores of 1 to 3, respectively. The number of participants were 153 in Fall 2015, 82 in Fall 2016, and 159 (the new record!) in Fall 2017. The number of first place votes are summarized in the following table.

COSTUME FALL 2015 FALL 2016 2015-16 TOTAL FALL 2017

Construction Barrel 53 23 76 75

Minion 72 45 11763

Baseball Player 28 14 42 21

TOTAL VOTES 153 82 235 159

(a) Treating the students in Fall 2016 and Fall 2015 as populations 1 and 2, respectively, Dr. Farrell computed an approximate 90% confidence interval for the difference in the proportions of Fall 2016 and Fall 2015 students whose first choice was the construction barrel to be (-0.17, 0.04). Would this result suggest a difference in these two proportions? Explain.

(b) Based on the result in (a), suppose we combine the results from 2015 and 2016, yielding 76 students out of 235 who chose the construction barrel as their first choice. Compute a 90% confidence interval for the difference in the population proportion of Fall 2017 students and the population proportion of combined 2015-16 students whose first choice was the construction barrel, and interpret your result. Would it appear from your interval that the percentage of students who chose the construction barrel was different in 2017 compared to 2015-16?

(c) It is stated above that students were always presented with pictures of the costumes in the same order (construction barrel, minion, baseball player). Give one concern that you might have with this approach, and recommend an alternative method that could have been used.

(d) Comment briefly on the procedure that Dr. Farrell used to sample students (voluntary participation), and whether it is consistent with the assumed approach for sample selection. HINT: At times, we may not be able to adhere to all the assumptions for a given procedure. This does not necessarily imply that we should not use it, but we should, however, acknowledge and discuss the limitations in doing so.