A group of 12 students were instructed in calculus using traditional methods. At the end of the course these students were given a standardized test to determine their understanding of calculus. The average score of these 12 students on the test was 69.5 with a standard deviation of 8.54. A separate group of 10 students were taught calculus using a new experimental teaching method. The average score on the standardized test given at the end of the course was 79.6 with a standard deviation of 9.29. Using this information, find a 95% confidence interval for the difference in population mean scores on the standardized test of the two teaching methods. Choose the best answer below:

i) (-12.86, -7.59)

ii) (-17.71, -2.69)

iii) (-18.04, -2.16)

iv) (-12.71, -7.69)

v) none of these