Question: A group of 25 ulcer patients is found to have a mean score of 45 and a standard deviation of 10 on a measure of repressed anger. A hypothesis testing is being conducted to see if the mean for all ulcer patients is different from the population mean of \[\text{42}.\text{5}\].

(a) State the null hypothesis and alternative hypothesis in mathematical notations.

(b) Find the test statistic.

(c) For a two-tailed test with a = 2%, what are the critical values?

(d) What should the researcher decide given the above results?

(e) If the researcher's conclusion above is an error, what type of error would that be?