Question

Using the accompanying Colleges and Universities data to find​ 95% confidence intervals for the median SAT for each of the two​ groups, liberal arts colleges and research universities. Based on these confidence​ intervals, does there appear to be a difference in the median SAT scores between the two​ groups?

For the liberal art​ colleges, the​ 95% confidence interval is

For the research​ universities, the​ 95% confidence interval is

Liberal Arts Colleges Median SAT score	Research Universities Median SAT score
1163	1115
1203	1147
1196	1165
1200	1186
1211	1200
1214	1213
1221	1220
1229	1221
1230	1234
1240	1276
1255	1272
1260	1283
1254	1289
1251	1274
1249	1284
1255	1292
1281	1310
1288	1320
1299	1349
1302	1359
1299	1360
1314	1366
1314	1373
1328	1395
1326

Answer 1

using t test in minitab for two samples

we have

Two-sample T for Liberal Arts Colleges Median SA vs Research Universities Median SA

   N Mean StDev SE Mean
Liberal Arts Colleges Median SAT score   25 1255.3 45.3 9.1
Research Universities Median SAT score 24 1271.0 76.5 16

Difference = μ (Liberal Arts Colleges Median SAT score ) - μ (Research Universities Median SAT score)
Estimate for difference: -15.7
95% CI for difference: (-52.3, 20.9)

since the confidence interval contains 0 so does not appear to be a difference in the median SAT scores between the two​ groups