A drug company has developed a new formulation of a popular pain reliever. It appears that the new formula provides quicker pain relief than the old formula, which provided relief in 15 minutes, on average. The company wants to gather evidence to see if the new drug provides relief faster than the old one.
a. What should the null and alternative hypotheses be for this situation?
b. Explain the Type I and Type II errors in the context of the pain reliever.
c. If the company reported that it had rejected the null hypothesis at a 10% significance level, would you be inclined to switch to the new drug for faster pain relief? Why or why not?
d. If the company reported that it had rejected the null hypothesis, and that the test had a p-value of 1%, would you be inclined to switch to the new drug? Why or why not?