Question

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 0.10 significance level.

(a) The claim is that the mean difference (x - y) is greater than 25 (μd > 25). What type of test is this? This is a two-tailed test.This is a left-tailed test.    This is a right-tailed test. (b) What is the test statistic? Round your answer to 2 decimal 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 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 25 points.There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points.    We reject the claim that retaking the SAT increases the score on average by more than 25 points.We have proven that retaking the SAT increases the score on average by more than 25 points.

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

Answer 1

x	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
	Mean	31.71429
	SD	15.96793