(a) Use a chi-squared test to determine whether the scores for the 90044 students are distributed significantly differently to the UNSW distribution. State the hypotheses, the value of the test statistic and critical cut-off point (or alternatively, p-value) and conclusion. Use the bins/categories given in the table above and ? = 5%. List the assumptions of this chi-squared test and explain if you violated any of these assumptions. (Use R studio)

We collected the following 20 scores from 90044 students: (66%, 62%, 61%, 62%, 57%, 53%, 68%, 57%, 73%, 58%, 57%, 62%, 57%, 69%, 65%, 53%, 59%, 58%, 64%, 69%) According to the UNSW research team, participant scores are distributed as follows: Score = 60% [61%,64%] [65%, 68%] [69%, 71%] 272% Percentage of people with 50% 25% 15% 5% 5% score