Question

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 27 points. Test this claim at the 0.01 significance level.

(a) The claim is that the mean difference (x - y) is greater than 27 (μd > 27). What type of test is this? This is a right-tailed test. This is a left-tailed test.     This is a two-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. td = (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 H0 fail to reject H0     (e) Choose the appropriate concluding statement. The data supports the claim that retaking the SAT increases the score on average by more than 27 points. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 27 points.    We reject the claim that retaking the SAT increases the score on average by more than 27 points. We have proven that retaking the SAT increases the score on average by more than 27 points.

Senior Score (x) Junior Score (y) (x - y) 1137 1107 30 1285 1246 39 1317 1262 55 1220 1209 11 1154 1114 40 1085 1074 11 1130 1127 3 1323 1276 47 1215 1166 49 1225 1214 11 1096 1055 41 1266 1227 39 1252 1209 43 1118 1086 32 1104 1066 38 1127 1096 31 1324 1269 55 1187 1161 26 1111 1074 37 1177 1142 35 1161 1138 23 1263 1231 32 1304 1275 29 1098 1075 23 1193 1154 39 1113 1081 32 1201 1148 53 1181 1163 18 1062 1054 8 1106 1076 30 1170 1148 22 1098 1053 45 1249 1171 78 1261 1241 20 1083 1085 -2

Answer 1