Many high school students take the SAT's twice; once in theirJunior year and once in their Senior year. The Senior year scores(x) and associated Junior year scores (y) aregiven in the table below. This came from a random sample of 35students. Use this data to test the claim that retaking the SATincreases the score on average by more than 25 points. Test thisclaim at the 0.10 significance level.

(a) The claim is that the mean difference (x - y)is greater than 25 (μd > 25). Whattype of test is this? This is a two-tailed test.This is a left-tailedtest.    This is a right-tailed test. (b) What is the test statistic? Round your answer to 2decimal places. t d = (c) Use software to get the P-value of the test statistic.Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0fail to rejectH0     (e) Choose the appropriate concluding statement. The data supports the claim that retaking the SAT increases thescore on average by more than 25 points.There is not enough data tosupport the claim that retaking the SAT increases the score onaverage by more than 25 points.    We rejectthe claim that retaking the SAT increases the score on average bymore than 25 points.We have proven that retaking the SAT increasesthe score on average by more than 25 points.    Â

     Senior Score (x) Junior Score (y) (x - y) 1265 1238 27 1150 1110 40 1225 1174 51 1081 1070 11 1264 1224 40 1220 1205 15 1108 1102 6 1321 1274 47 1317 1264 53 1177 1167 10 1102 1063 39 1291 1252 39 1235 1195 40 1091 1060 31 1097 1062 35 1101 1073 28 1278 1222 56 1214 1187 27 1100 1061 39 1101 1066 35 1240 1217 23 1216 1183 33 1120 1091 29 1295 1273 22 1131 1095 36 1293 1263 30 1174 1122 52 1212 1193 19 1124 1116 8 1114 1084 30 1109 1087 22 1177 1134 43 1151 1076 75 1289 1267 22 1061 1064 -3