Retaking the SAT (Raw Data, Software Required): Many high school students take t

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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 25 points. Test this claim at the 0.05 significance level.

This is a two-tailed test.

This is a left-tailed test.    

This is a right-tailed test.

d

reject H0

fail to reject H0    

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.

(a) The claim is that the mean difference (x - y) is greater than 25 (d > 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 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 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) 1250 1222 28 1160 1119 41 1324 1273 51 1274 1260 14 1173 1136 37 1135 1123 12 1141 1138 3 1197 1151 46 1232 1182 50 1186 1173 13 1282 1242 40 1289 1247 42 1151 1108 43 1299 1269 30 1102 1067 35 1172 1142 30 1230 1175 55 1280 1251 29 1166 1128 38 1303 1269 34 1129 1104 25 1166 1132 34 1278 1245 33 1261 1239 22 1262 1225 37 1115 1084 31 1226 1176 50 1251 1231 20 1127 1119 8 1303 1276 27 1240 1218 22 1122 1079 43 1127 1053 74 1229 1208 21 1172 1174 -2

Explanation / Answer

a) Since alternative hypothesis contains ">" sign, this is a right tailed test.

Option 3 is correct.

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Senior Score (x) and Junior Score (y)
H0 : D = 25
HA : D > 25
Hypothesis test results:

b) td = 2.60

c) p - value = 0.0068

d) Reject Ho.

e) The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

Option 1 is correct.

Difference Mean Std. Err. DF T-Stat P-value Senior Score (x) - Junior Score (y) 31.885714 2.6440901 34 2.6041905 0.0068

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