A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys.

a. Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.
b. Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they are can be linked.
c. 1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.
d. Two-sample t-test. There is no natural pairing between the two populations.

A two-sample t - test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant.

Independent samples are samples that do not affect one another. The mean math scores of the samples of boys and girls do not affect each other. They are independent samples, hence the correct test procedure is two - sample t - test