Although there is popular believe that herbal remedies such as melatonin can decrease the time it takes to fall asleep these effects are typically not supported in a controlled study. The average individual takes 13 minutes to fall asleep with a standard deviation of 3 minutes. A researcher obtained a sample of 25 individuals and gave them a standard dose of melatonin before sleep. The sample participants fell asleep in an average of 11. 5 minutes. The researcher wishes to test the claim that individuals taking melatonin fall asleep faster than those not taking the supplement.

Compute the test statistic for the researchers data assuming the data can be modeled with a normal distribution?