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?

Liberal Arts Colleges Median SAT score   Research Universities Median SAT score
1160   1114
1188   1135
1196   1163
1193   1175
1214   1185
1227   1211
1223   1234
1241   1228
1241   1231
1239   1278
1248   1286
1258   1273
1246   1279
1247   1273
1258   1282
1251   1306
1280   1306
1285   1329
1294   1337
1301   1343
1293   1364
1305   1375
1318   1372
1327   1409
1333

Answer 1

First step, find sample size, mean and standard deviation of the two Median SAT scores data set.

Formula Reference:

95% Confidence interval for Liberal Arts Colleges Median SAT score:

Refer Column F for the calculation procedure and formulas used

95% CI for Liberal Arts Colleges Median SAT score (1235.89, 1273.39)

95% Confidence interval for Research Universities Median SAT score:

95% CI for Research Universities Median SAT score is (1236.88, 1303.79)

does there appear to be a difference in the median SAT scores between the two​ groups?

yes, there is difference in the interval between two groups.

Upper limit of the both confidence intevals are different. more over Research Universities Median SAT scores upper limit is much higher than the Liberal Arts Colleges Median SAT score