Question

This discussion question focus on selecting significance levels in order to avoid Type I or Type II errors. While we wish to avoid both types of errors, in practice we have to accept some trade-off between them. We could reduce the chance of making a Type I error by making it very hard to rejectH0, but then we would probably make Type II errors more often. On the other hand, if we routinely reject H0, we would rarely be guilty of a Type II error, but we would end up rejecting too manyH0’s that were actually true. For each situation described below, indicate whether it makes more sense to use a relatively large significance level (such asα= 0.1) or a relatively small significance level (such asα= 0.01). (1) Using a sample of 10 games each to see if your average score at Wii bowling is significantly more than your friends’s average score. (2) Testing to see if a well-known company is lying in its advertising. If there is evidence that the company is lyidng, the Federal Trade Commission will file a lawsuit against them. (3) Testing to see whether taking a vitamin supplement each day has significant health benefits. There are no known harmful side effects of the supplement.

Answer 1

(1)

Null Hypothesis:

My average score at Wii bowling is not significantly more than my friends’s average score.

Alternative Hypothesis:

My average score at Wii bowling is significantly more than my friends’s average score.

In this case, it makes more sense to use a relatively small significance level because small significance level means the probability of rejecting the true null hypothesis is small.

This increases the type 2 error which is the probability of "failing to reject the null hypothesis when it is false" and it's fine not to reject the false null hypothesis, in this case, because it makes me improve. (since not rejecting the null hypothesis means that there is no evidence to claim my average score is significantly greater than that of my friend's and so, I will try to improve).