Retaking the SAT (Raw Data, Software Required): Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. The Senior year scares (x) and associated Junior year stores (7) are given in the table below. This came from a random sample at 35 students. Use this data to test the claim that retaking the SAT increases the stare on auerage hy more than 27 points. Test this claim at the 0.015lgnicanca level. (a) The claim is that the mean ditferehce (xi y) is greater than 27 (21,, > 27). what type dftest is this? Sen'rlfsgre (*3 \"maria? (V) \"(2'3\" 0 Thi5lsatwmlal'ad test. 1268 1225 43 o This is a righttailed test. 1203 \"49 54 O T1115 is a \\efbtailed test. 1099 1087 12 1315 1277 33 (b) What is [he lest Stalistlc? Round vnllr answer 10 2 decimal placgi. 1166 1151 15 t; : 1098 1092 6 1312 1255 47 (c) Use software to et the Psvmue 0f the test statistic. Rnuml lo 4 decimal places. 1116 1055 51 P-Va'ue = 1i 1228 127d 10 (d) what is the conclusion regarding the null hypothesis? 11:3 is: :i O \"'2\" H\" 1143 1102 41 O fail to reject Hu was 1050 30 1120 1052 33 (e) Cheese the apnrnpriate concluding statement. 1125 1095 3\" O The data supports the claim that retaking the SAT increases the score on average by more than 27 nointa. 1134 107d 56 c There is not enough data to support the claim that retaking the SAT ln(reases the score on average by mere than 27 points. 1192 1'55 25 0 We reject the claim that relalu'ng the SAT increases the scare an average by more than 27 points. ii: 13:: :3 0 We have nroven that retaking the SAT increases the score on average by more than 27 points. 1253 1239 25 1151 1125 35 1278 1247 31 1132 1106 26 1271 1234 37 1198 1159 29 1102 1050 52 1275 1256 19 1276 1266 s 1158 1128 3D 1271 1249 22 1256 1220 45 1251 1176 75 1241 1222 19 1268 1269 .1