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 35students. 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 0.10 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 right-tailed test.      This is a two-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) 1136 1105 31 1316 1276 40 1187 1133 54 1292 1278 14 1297 1256 41 1219 1205 14 1077 1072 5 1234 1186 48 1124 1074 50 1074 1062 12 1167 1127 40 1310 1268 42 1108 1067 41 1086 1054 32 1137 1099 38 1311 1279 32 1104 1050 54 1161 1133 28 1149 1111 38 1107 1070 37 1122 1098 24 1251 1217 34 1279 1247 32 1176 1154 22 1236 1198 38 1208 1178 30 1115 1065 50 1294 1275 19 1237 1230 7 1260 1230 30 1117 1096 21 1291 1248 43 1156 1078 78 1221 1201 20 1113 1114 -1

Answer 1

The statistical software output for this problem is:

One sample T hypothesis test: H Mean of variable Ho H27 HA : H 27 Hypothesis test results: Variable Sample Mean Std. Err. DF P-value T-Stat (x- y) 0.0249 32.514286 2.7101959 34 2.0346447

Hence,

a) Right Tailed Test

b) t = 2.03

c) P - value = 0.0249

d) Reject Ho

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