Opdracht 10b ------------ t-procedures for paired data t-procedures for independent samples pooled t-procedures for two independent samples Two groups, each consisting of 10 teachers of Spanish, followed an intensive suumer school course in Spanish. Before and after the course they underwent a listening test. The table below gives the scores before and after the course. (Data courtesy of Joseph A. Wipf, Department of Foreign Languages and Literatures, Purdue University.) Group After Before 1 29 30 1 30 28 1 32 31 1 30 26 1 16 20 1 25 30 1 31 34 1 18 15 1 33 28 1 25 20 2 32 30 2 28 29 2 34 31 2 32 29 2 32 34 2 27 20 2 28 26 2 29 25 2 32 31 2 32 29 The data are available in z:\public\share\heeringa\luister.txt. Read this ASCII-file in. Define the three columns of the table and choose the variable names 'group' ('groep'), 'before' ('vooraf') and 'after' ('achteraf'). a. Draw a normal-quantile plot for the scores before and draw a second normal-quantile plot for the scores after. b. Give a 90%-confidence interval for the average increase of the scores of the auditory exam, an increase due to attending the summer school. Do not differentiate between group 1 and group 2. c. Is the increase in scores significant? Formulate the appropriate H_0 (null hypothesis) and H_a (alternative hypothesis). Do not distinguish between group 1 and group 2. d. Draw a normal-quantile plot for the group 1 scores before and draw a second normal-quantile plot for the group 2 scores before. e. Give a 90%-confidence interval for the difference in averages of the 'scores before' of group 1 versus group 2. Assume that the standard deviations of the two populations are not equal. f. Is there a significant difference between the average 'score before' of group 1 and the average 'score before' of group 2? Formulate the appropriate H_0 and H_a. Assume that the standard deviations of the two populations are not equal. g. Give a 90%-confidence interval for the difference in averages of the 'score before' of group 1 and the 'score before' of group 2. Assume that the standard deviations of the two populations are not equal. h. Is there a significant difference between the average 'score before' of group 1 and the average 'score before' of group 2? Formulate the appropriate H_0 and H_a. Assume that the standard deviations of the two populations are not equal.