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 0.10 significance level.

(a) The claim is that the mean difference (x - y) is greater than 27 (μ_d > 27). What type of test is this?

This is a right-tailed test.

This is a two-tailed test.    

This is a left-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t-a= ?

(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)
1285	1258	27
1228	1188	40
1176	1124	52
1238	1223	15
1246	1206	40
1070	1057	13
1265	1262	3
1268	1221	47
1263	1211	52
1217	1207	10
1221	1181	40
1178	1137	41
1188	1149	39
1189	1159	30
1201	1164	37
1116	1085	31
1181	1126	55
1078	1051	27
1266	1228	38
1309	1274	35
1173	1146	27
1191	1157	34
1129	1100	29
1205	1182	23
1132	1097	35
1199	1167	32
1266	1214	52
1124	1107	17
1072	1062	10
1284	1256	28
1100	1079	21
1191	1147	44
1146	1068	78
1124	1103	21
1109	1113	-4

Answer 1

using minitab>stat>basic stat>paired t test

we have

Paired T-Test and CI: Senior Score (x), Junior Score (y)

Paired T for Senior Score (x) - Junior Score (y)

N Mean StDev SE Mean
Senior Score (x) 35 1189.4 66.2 11.2
Junior Score (y) 35 1157.4 63.7 10.8
Difference 35 31.97 16.29 2.75

90% lower bound for mean difference: 28.37
T-Test of mean difference = 27 (vs > 27): T-Value = 1.81 P-Value = 0.0397

(a) The claim is that the mean difference (x - y) is greater than 27 (μ_d > 27). \

This is a right-tailed test.

(b) the test statistic(t) =1.81

(c)
P-value = 0.0397

(d) Since p value is less than 0.1 so 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.