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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 scores (x) and associated Junior year scores (y) are given in the table below. This came from a random sample of 35 students. Use this data to test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.01 significance level. (a) The claim is that the mean difference (x - y) is greater than 25 (ud > 25). What type of test is this? O This is a two-tailed test. Senior Score (x) |Junior Score (y) ( x - y) 1269 1239 O This is a left-tailed test. 30 1109 1070 39 This is a right- tailed test. 1285 1232 53 1147 1134 13 (b) What is the test statistic? Round your answer to 2 decimal places. 1261 1221 40 ta = 1157 1144 13 1135 1132 3 (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. 1154 1108 46 P-value = 1201 1149 52 1108 1094 14 (d) What is the conclusion regarding the null hypothesis? 1308 O reject Ho 1267 41 1290 1251 39 O fail to reject Ho 125 1215 42 1140 1110 30 (e) Choose the appropriate concluding statement. 1096 1059 37 O The data supports the claim that retaking the SAT increases the score on average by more than 25 points. 1098 1067 31 1305 O There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points. 1253 52 1194 1 167 We reject the claim that retaking the SAT increases the score on average by more than 25 points. 27 1206 1 168 38 O We have proven that retaking the SAT increases the score on average by more than 25 points. 1205 1 170 35 1 164 1141 23 1 167 1131 36 1264 1233 31 1234 1212 22 1 159 1123 36 1160 1127 33 1278 1228 50 1198 1181 17 1134 1125 9 1263 1232 31 1204 1181 23 1 146 1 101 45 1265 1187 78 1267 1246 21 1167 1171 -4