Step 1 :(a) The null hypothesis, denoted by \(H_{0}\), is a statement of no effect or no difference. In this case, the null hypothesis would be that the mean score is 148 (as reported by the website). The alternative hypothesis, denoted by \(H_{1}\), is what we are trying to prove, a statement that indicates the presence of an effect or difference. In this case, the alternative hypothesis would be that the mean score is not 148 (since we have reason to believe it differs). So, \(H_{0}: \mu = 148\) and \(H_{1}: \mu \neq 148\).
Step 2 :(b) If we reject the null hypothesis, we might be making a Type I error. This is when we incorrectly reject a true null hypothesis, i.e., we say there is an effect or difference when there actually isn't.
Step 3 :(c) A Type II error is when we fail to reject a false null hypothesis, i.e., we say there is no effect or difference when there actually is. Given that the true mean score is 141, a Type II error would be failing to reject the hypothesis that the mean score is 148 when, in fact, it is 141.