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 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 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) 1093 1063 30 1238 1195 43 1238 1186 52 1112 1099 13 1289 1248 41 1109 1098 11 1061 1055 6 1102 1056 46 1139 1087 52 1090 1076 14 1157 1118 39 1263 1223 40 1279 1240 39 1117 1086 31 1226 1191 35 1216 1187 29 1324 1268 56 1199 1173 26 1279 1244 35 1165 1128 37 1151 1124 27 1159 1124 35 1256 1224 32 1255 1231 24 1129 1093 36 1299 1270 29 1261 1207 54 1207 1187 20 1156 1147 9 1177 1150 27 1253 1234 19 1320 1274 46 1200 1122 78 1234 1213 21 1143 1143 0

Answer 1

(a)

This is a right-tailed test.

(b)

Following table shows the calculations:

X	Y	d=X-Y	(d-mean)^2
1093	1063	30	5.48918041
1238	1195	43	113.5737804
1238	1186	52	386.4015804
1112	1099	13	374.1477804
1289	1248	41	74.94538041
1109	1098	11	455.5193804
1061	1055	6	693.9483804
1102	1056	46	186.5163804
1139	1087	52	386.4015804
1090	1076	14	336.4619804
1157	1118	39	44.31698041
1263	1223	40	58.63118041
1279	1240	39	44.31698041
1117	1086	31	1.80338041
1226	1191	35	7.06018041
1216	1187	29	11.17498041
1324	1268	56	559.6583804
1199	1173	26	40.23238041
1279	1244	35	7.06018041
1165	1128	37	21.68858041
1151	1124	27	28.54658041
1159	1124	35	7.06018041
1256	1224	32	0.11758041
1255	1231	24	69.60398041
1129	1093	36	13.37438041
1299	1270	29	11.17498041
1261	1207	54	469.0299804
1207	1187	20	152.3471804
1156	1147	9	544.8909804
1177	1150	27	28.54658041
1253	1234	19	178.0329804
1320	1274	46	186.5163804
1200	1122	78	2084.57078
1234	1213	21	128.6613804
1143	1143	0	1046.06318
Total		1132	8757.885714

Sample size: n= 35

Now,

The test statistics is:

(c)

The p-value using excel function "=TDIST(1.97,34,1)" is: 0.0285

(d)

Since p-value is greater than 0.01 so we fail to reject the null hypothesis

fail to reject H0

(e)

The data supports the claim that retaking the SAT increases the score on average by more than 27 points.