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 27points. 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 left-tailed test.This is a two-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 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) 1284 1257 27 1121 1079 42 1132 1081 51 1091 1076 15 1121 1083 38 1276 1264 12 1203 1198 5 1155 1109 46 1189 1136 53 1103 1091 12 1219 1179 40 1246 1204 42 1301 1260 41 1115 1084 31 1167 1131 36 1131 1101 30 1308 1253 55 1279 1251 28 1236 1201 35 1186 1150 36 1289 1263 26 1287 1253 34 1107 1074 33 1131 1105 26 1156 1120 36 1310 1279 31 1225 1174 51 1174 1155 19 1209 1198 11 1077 1050 27 1179 1159 20 1193 1150 43 1247 1172 75 1143 1124 19 1176 1177 -1

Answer 1

	Senior Score (x)	Junior Score (y)	(x - y)
	1284	1257	27
	1121	1079	42
	1132	1081	51
	1091	1076	15
	1121	1083	38
	1276	1264	12
	1203	1198	5
	1155	1109	46
	1189	1136	53
	1103	1091	12
	1219	1179	40
	1246	1204	42
	1301	1260	41
	1115	1084	31
	1167	1131	36
	1131	1101	30
	1308	1253	55
	1279	1251	28
	1236	1201	35
	1186	1150	36
	1289	1263	26
	1287	1253	34
	1107	1074	33
	1131	1105	26
	1156	1120	36
	1310	1279	31
	1225	1174	51
	1174	1155	19
	1209	1198	11
	1077	1050	27
	1179	1159	20
	1193	1150	43
	1247	1172	75
	1143	1124	19
	1176	1177	-1
Mean	1193.314286	1161.171429
		Mean (x-y)	32.14286

SD

15.60004

a) μ > 27 which means right tailed test

b)t = (Mean(X-Y) - μ) / (s/√n)

t = (32.14 - 27)/(15.6/√35)

t = 5.14/2.6369

t = 1.95

c) The p-value is .0297.

The result is not significant at p < .01.

d) Fail to reject null hypothesis

e) There is not enough data to support the claim that retaking the SAT increases the score on average by more than 27 points