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

(a) The claim is that the mean difference (x - y) is greater than 25 (μd > 25). What type of test is this? This is a two-tailed test. This is a right-tailed test.     This is a left-tailed test. (b) What is the test statistic? Round your answer to 2 decimal places. td = (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) 1101 1073 28 1128 1085 43 1310 1255 55 1285 1274 11 1229 1188 41 1199 1184 15 1222 1216 6 1103 1056 47 1148 1095 53 1134 1123 11 1227 1186 41 1146 1104 42 1313 1270 43 1163 1131 32 1282 1248 34 1115 1084 31 1109 1056 53 1220 1194 26 1176 1141 35 1101 1064 37 1153 1130 23 1090 1057 33 1217 1186 31 1197 1174 23 1249 1212 37 1183 1154 29 1289 1236 53 1125 1108 17 1103 1092 11 1188 1160 28 1174 1152 22 1260 1213 47 1181 1107 74 1146 1126 20 1274 1278 -4

Answer 1

Answer Date: 11/11/2019 To test the hypothesis is that retaking the SAT increases the score on average by more than 25 points at 5% significance level. The null and alternative hypothesis is, Ho: la = 25 H:Ha > 25 The hypothesis test is right-tailed test. b) The t-test statistics is, By using Excel software, find t-test statistics with the help of following steps: Import the data. 2) Select t-test: Paired Two Samples for Means from Data Analysis in Data menu. 3) Select Variable 1 Range and Variable 2 Range.

5) Give Hypothesized Mean Difference. Select Labels and give Alpha. Choose Output Range from Output options. Click Ok. 7) t-Test: Paired Two Sample for Means Senior Score (x) Junior Score (y) 1186.857143 1154.628571 4419.831933 4585.887395 35 35 0.971013113 Mean Variance Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 34 2.639327883 0.006223781 1.690924198 0.012447563 2.032244498 From the Excel output, the t-test statistics is 2.64.

The p-value for this test is, From the Excel output in part (b), the p-value for this test is 0.0062) Decision The conclusion is that p-value in this context is less than 0.05 which is 0.0062, so the null hypothesis is rejected at 5% level of significance. e) There is sufficient evidence to indicate that retaking the SAT increases the score on average by more than 25 points. The result is statistically significant. The answer option is 1.