Question

For each situation described, indicate whether it makes more sense to use a relatively large significance level (such as \(\alpha=0.10\) ) or a relatively small significance level (such as \(\alpha=0.01\) ). Using a sample of 10 games each to see if your average score at Wii bowling is significantly more than your friend's average score.

Short answer

In this context, it would make more sense to use a relatively large significance level, such as \(\alpha = 0.10\).

Step-by-step solution

Understand the context

We're investigating whether the average score in Wii bowling is significantly more than the friend's average score. Therefore, it's a friendly competition and the truth of whether one person scores higher on average does not have serious real-world consequences.

Assess the potential consequences of a false positive result

Here, falsely deciding that your score is higher on average (a false positive) would only result in a minor mishap, as it only concerns a friendly competition. No one would be terribly hurt by it.

Decide the appropriate significance level

Given that the potential consequences of a false positive result are minor, it is less crucial to require a lot of evidence before deciding that your score is higher on average. Therefore, it would make more sense to use a relatively large significance level, such as \(\alpha = 0.10\), as it requires less evidence to reject the null hypothesis (your friend's average score is the same or more than yours).