Q10. Here are the final marks of two separate cohorts of students undertaking an intelligence test (100 is intelligent). (25 marks) Student Scores Cohort A Cohort B 5 45 10 40 40 55 50 60 25 50 70 55 5 75 95 20 (a) What are the mean median and mode scores for both cohorts? (b) If the Sum of Squared Deviations (SY) is given by SY = (Y - )2, where is the mean of the data set, calculate SY for both cohorts. Include your full calculations; they count as part of your answer!! (c) What is the relationship between Sum of Squared Deviations and variance? (d) What do the variances of the two cohorts tell you about the cohorts? (e) If you were fitting those data to bell shaped probability curve(s), what would the curve(s) look like? (f) What does the null hypothesis say about these two cohorts?

(g) Should I use an unpaired t-test, a paired t-test, a t-test that assumes equal variances or a t- test that doesnt assume equal variances to compare the data and why??

(h) If we were to compare the means of the two data sets and P was found to be less than 0.05, what would it mean? (i) If the means of the populations are not significantly different, does it mean that the populations are the same? Why?