Notes

1. A larger sample size gives more information about the true parameter, making it more likely to detect the alternative hypothesis if it is true. If Mr. Y took 1,000 free throws instead of 50, it would become much easier to decide against his 80% claim if he wasn’t really that good.
2. Using a larger significance level makes it easier to reject H0​ (remember that α tells us how likely it is we would reject H0​), which is needed for more Power.
3. It is easier to detect a bigger difference between the null and alternative parameter value. If Mr. Y was actually a 22% free throw shooter, a sample of 50 free throws would undoubtedly lead us to reject the claim that he is an 80% free throw shooter.

• Increasing α will increase the probability of a Type I error. But it will also increase the Power, meaning that it will decrease the probability of a Type II error. Do this if the consequences of the Type II error are more serious.
• Decreasing α will decrease the probability of a Type I error. But it will also decrease the Power, meaning that it will increase the probability of a Type II error. Do this if the consequences of the Type I error are more serious.