Step 1 :Calculate the differences between the scores before and after the prep course for each student. The differences are as follows: \(1170 - 1060 = 110\), \(1550 - 1410 = 140\), \(1360 - 1170 = 190\), \(1410 - 1130 = 280\), \(1390 - 1180 = 210\), \(1300 - 1190 = 110\), \(1520 - 1280 = 240\), \(1320 - 1290 = 30\), \(1210 - 1200 = 10\)
Step 2 :Calculate the mean difference: \(\frac{110 + 140 + 190 + 280 + 210 + 110 + 240 + 30 + 10}{9} = \frac{1420}{9} = 157.78\)
Step 3 :Calculate the standard deviation: \(\sqrt{\frac{(110-157.78)^2 + (140-157.78)^2 + (190-157.78)^2 + (280-157.78)^2 + (210-157.78)^2 + (110-157.78)^2 + (240-157.78)^2 + (30-157.78)^2 + (10-157.78)^2}{8}} = \sqrt{\frac{64128.56}{8}} = \sqrt{8016.07} = 89.53\)
Step 4 :Calculate the test statistic: \(\frac{157.78 - 60}{89.53 / \sqrt{9}} = \frac{97.78}{29.84} = 3.276\)
Step 5 :\(\boxed{\text{The value of the test statistic is 3.276}}\)