1. [Maximum mark: 27] Two IB schools, A and B, follow the IB Diploma Programme but have different maching methods. A research group tested whether the different teaching methods lead to a similar nal result. For the test. a group of eight students were randome selected from each school. Both samples were given a standardized test at the start of the course and a prediction for total IB points was made based on that test; this was then compared to their points total at the end of the course. Previous results indicate that both the predictions from the standardized tests and the nal IB points can be modelled by a normal distribution. It can be assumed that: - the standardized test is a valid method for predicting the nal IB points - that variations from the prediction can be explained through the circumstances of the student or school. (a) Identify a test that might have been used to verify the null hypothesis that the predictions from the standardized test can be modelled by a normal distribution. [1] (b) State why comparing only the nal [3 points of the students from the two schools would not be a valid test for the effectiveness of the two different teaching methods. [1] (T his question continues on the following page) The data for school A is shown in the following table. School A Student number Gender Predicted IB points (p) Final IB points (f) 1 male 43.2 44 2 male 36.5 34 3 female 37.1 38 4 male 30.9 28 5 male 41.1 39 a female 35.1 39 male 36.4 40 8 male 38.2 38 Mean 37.31 37.5 (c) For each student, the change from the predicted points to the final points ( f -p) was calculated. (i) Find the mean change. (ii) Find the standard deviation of the changes. [3] (d) Use a paired t-test to determine whether there is significant evidence that the students in school A have improved their IB points since the start of the course. [4] W.satprep.co (This question continues on the following page)1 The data for school B is shown in the following table. (9) (i) (ii) School B Student number Gender Pmdii'itzzllglfczrgffp) 1 male 8.? 2 female 1 . 1 3 female 4.8 4 female 1 .5 5 male 2.5 1 I 6 female 3.2 7 female 1 .3 8 female 3. 1 ' Mean 2.3 Use an appropriate test to determine whether there is evidence, at the 5 % signicance level, that the students in school B have improved more than those in school A. State why it was important to test that both sets of points were normally distributed. (This question continues on the following page) [5] - 5 - SPECfMATAIfHPSfENGITZOfXX (Question 1 continued) School A also gives each student a score for effort in each subject. This effort score is based on a scale of 1 to 5 where 5 is regarded as outstanding effort. - - - -_-_ - It is claimed that the effort put in by a student is an important factor in improving upon their predicted IB points. if) (i) Perform a test on the data from school A to show it is reasonable to assume a linear relationship between effort scores and improvements in IE points. You may assume effort scores follow a normal distribution. (ii) Hence. nd the expected improvement between predicted and nal points for an increase of one unit in effort grades. giving your answer to one decimal place. [4] Amathematics teacher in school A claims that the comparison between the two schools is not valid because the sample for school B contained mainly girls and that for school A. mainly boys. She believes that girls are likely to show a greater Improvement from their predicted points to their nal points. She collects more data from other schools. asking them to class their results into four categories as shown in the following table. (g) Use an appropriate test to determine whether showing an improvement is independent of gender. [6] (h) If you were to repeat the test performed in part (e) intending to compare the quality of the teaching between the two schools. suggest two ways in which you might choose your sample to improve the validity of the test. [2] Turn over