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

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.

1. This is a left-tailed test.
2. This is a two-tailed test.    
3. This is a right-tailed test.

1. reject H0
2. fail to reject H0    

1. The data supports the claim that retaking the SAT increases the score on average by more than 27 points.
2. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 27 points.    
3. We reject the claim that retaking the SAT increases the score on average by more than 27 points.
4. 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) 1248 1217 31 1179 1139 40 1254 1201 53 1117 1102 15 1140 1103 37 1208 1196 12 1063 1060 3 1177 1129 48 1223 1172 51 1168 1157 11 1277 1236 41 1104 1063 41 1255 1212 43 1145 1116 29 1094 1059 35 1238 1210 28 1222 1168 54 1256 1226 30 1230 1191 39 1131 1096 35 1121 1094 27 1247 1213 34 1262 1230 32 1076 1052 24 1223 1186 37 1291 1262 29 1149 1098 51 1126 1108 18 1232 1222 10 1261 1232 29 1219 1199 20 1273 1228 45 1129 1055 74 1075 1056 19 1181 1181 0

Explanation / Answer

H0 : ?x-y <= 27

Ha : ?x-y > 27

(A) The test is right - tailed test. Option 3 is correct.

(B) Here dbar = 32.1429

stadnard deviation of difference sd = 15.74455

standard error of difference sed = sd /sqrt(n) = 15.74455/sqrt(35) = 2.6613

Here test statitic

t = (dbar - 27)/sed = (32.1429 - 27)/2.6613 = 1.932

(c) P- value = 0.0308 < 0.10

(d) We reject the null hypothesis.

(e) Here correct stateemnt is  "The data supports the claim that retaking the SAT increases the score on average by more than 27 points."

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.