BED2126 BASIC SOCIAL STATISTICS CAT 1 and 2 1 A group of twelve children participate in a psychological study designed to assess the relationship if any between age x years and average total sleep time ATST y minutes To obtain a measure of ATST recordings were taken on each child on five consecutive rights and then averaged The results obtained are shown in the below Child Age x years ATST y minutes A B C D E F G H K L 4 4 6 7 10 5 9 6 12 4 5 5 11 1 8 6 14 0 10 1 7 2 7 9 586 565 515 532 478 560 493 533 575 490 530 515 a Draw a scatter diagram and determine the regression between age and ATST 8 Marks This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx I J This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx K 7 2 530 3816 51 84 280900 This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx L 7 9 108 515 6372 4068 5 62 41 265225 56825 4 1060 1 3396942 a 6372 1060 1 108 56825 4 12 1060 1 1082 584 39 b 12 56825 4 108 6372 12 1060 1 1082 5 93 y 584 39 5 93x Regression equation b Calculate the value of the moment correlation coefficient between x and y Assess the statistical significance of your value and interpret your results 12 Marks r n x y x y n x 2 x 2 n y 2 y 2 r 12 56825 4 108 6372 12 1060 1 1082 12 3396942 63722 0 48 Moment correlation coefficient of 0 48 indicates weak negative correlation meaning the variables tend to move in different direction When Y Increases X decreases To test statistical significance we need to define the null and the alternative hypothesis use 5 significance level for two tailed Using critical values tables for n 12 0 576 meaning the critical region where H0 is rejected is r 0 576 and r 0 576 Therefore we have sufficient evidence to reject the null hypothesis since r 0 48 2 The table below shows frequency distribution which represents weights of books purchased by customers who visited a book show in one day Weight in gm 110 119 No of customers 5 This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx x y x y H0 r 0 H1 r 0 We r critical This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx Median 140 7 6 147 6 This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx Median 147 6 1 0 2 0 0 c interval range 1 This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx 2 Marks Mode is 146 iii The mode m l f 1 f 0 2f1 f0 f2 c l modal class lower limit f modal class frequency f frequency preceding the modal class f frequency succeeding the modal class The highest frequency is 20 and is within interval 140 149 l 140 f 20 f0 12 f2 16 c 9 m 140 20 12 2 20 12 16 9 146 Powered by TCPDF www tcpdf org This study source was downloaded by 100000780346594 from CourseHero com on 04 14 2021 12 10 59 GMT 05 00 https www coursehero com file 67047640 DED1204 Basic Social Statistics CATediteddocx