calculate the mean length of group1 songs minus the mean length of group2 songs.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

QUESTIONS

Define group 1 to be all songs before 1980 (so, 1979 and earlier), and group 2 to be songs from 1990 onward. For brevity of expression, in this assignment we call group 1 "old songs" and group 2 "new songs". Throughout, we use significance level alpha=5%. 

Q1: calculate the mean length of group1 songs minus the mean length of group2 songs.

Q2: with the same order (group1 minus group 2), calculate the difference between median song lengths.

Q3: find difference between the mean vocabulary size of the two groups.

Q4: find the difference between median vocabulary size of the two groups. 

Q5: We want to test the hypothesis: average length of old songs is different from average length of new songs.

conduct a permutation test with 50'000 permutations. What are the critical values? 

Q6: We want to test the hypothesis: average length of old songs is less than average length of new songs.

conduct a permutation test with 50'000 permutations. What is the critical value? 

Q7: We want to test the hypothesis: median length of old songs is less than median length of new songs.

conduct a permutation test with 50'000 permutations. What is the critical value? 

Q8: Now let's focus on vocabulary size instead of song length. 

We want to test the hypothesis: median vocabulary size of old songs is less than median vocabulary size of new songs.

conduct a permutation test with 50'000 permutations. What is the critical value? 

Now define a new variable, which we call "word density", to be:  s o n g v o c a b u l a r y s i z e /s o n g l e n g t h   

Q9: We want to test the hypothesis: median word density of old songs is different from median word density of new songs.

conduct a permutation test with 50'000 permutations. What are the critical values? 

Q10: We want to test the hypothesis: average word density of old songs is different from average word density of new songs.

conduct a permutation test with 50'000 permutations. What are the critical values?

 

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