A growing body of studies challenges conventional assumptions that genetics or cultural differences lead some students - such as indigenous or girls to do poorly on standardised academic tests and other academic performances. To examine the phenomenon associated with "stereotype threat", researchers gave 48 randomly selected indigenous students a standardised test, asking students to indicate their ethnicity before taking the test (First Week). In the second week, students were given the same test but this time without revealing their race (Second Week). On a 100-point scale, students' test scores were recorded in the EXCEL file Standardised Tests.xlsx. Use EXCEL and an appropriate hypothesis test to help researchers to answer the following research question. Research Question: Was a negative stereotype activated simply by calling attention to one's race that might impact students' test performance? Frequency 0 5 10 15 Frequency T 0 5 10 15 20 Figure 1: First Week Histogram Figure 3: Histogram of Differences (First-Second) Frequency 5 10 15 Figure 2: Second Week Histogram 60 65 70 75 80 85 60 65 70 75 80 85 Test Scores Test Scores -20 -15 -10 -5 0 5 10 15 Test Scores Test Scores 65 70 75 80 85 Figure 4: Boxplots of Test Scores First Week Second Week Answer the following questions by choosing the most correct option or typing the answer: 1. (1 mark) The most appropriate test for these data is: 2. (1 mark) Which graphical display would be useful to check normality assumption for this hypothesis? A. Figure 1 B. Figure 2 C. Figure 3 D. Figure 4 E. Figure 1 & 2 F. Figure 3 & 4 G. No need to check normality assumption H. All four figures are needed 3. (1 mark) How can you check the assumption of equal variances? A. Comparative boxplots could be used (e.g. if the sizes of boxes are similar or not) B. Descriptive statistics such as variance, standard deviation and range could be used C. Descriptive statistics such as mean and median could be used D. The histogram of differences could be used E. Both A & B could be used F. No need to check the assumption of equal variances For the remaining questions you may assume that any relevant assumptions have been met. 4. (2 marks) The absolute value of the test statistic is equal to 5. (1 mark) The degrees of freedom is equal to 6. (1 mark) The p-value is larger than 0.05 7. (2 marks) The test shows that the test scores were (Integer) (3dp) A. significantly different between the First Week and the Second Week, possibly higher in the First Week. B. significantly different between the First Week and the Second Week, possibly higher for the Second Week. C. not significantly different between the two weeks. 1 FirstWeek SecondWeek 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 27622522222222222226230245227222677077372166232 74 82 69 81 66 63 84 78 79 78 73 78 75 74 72 78 68 76 77 84 70 84 68 78 81 78 80 78 68 81 77 70 85 77 74 78 76 69 74 72 81 77 71 81 71 68 82 78 74 71 83 76 76 74 81 76 78 68 74 77 81