The coach of a swimming team wonders if a new swim cap will make their team swim faster than their existing caps. The coach has each swimmer complete two laps—one with the new cap and one with their existing cap (in a random order). They want to test if, on average, the times are lower with the new caps.
What type of statical test used in this case?

A. A two-sample z-test for the difference of proportions
B. A χ2 goodness of fit test
C. A paired t-test for the mean difference
D. A z-test for a proportion
E. A two-sample t-test for the difference of means