A psychulugist was interested in knowing whether male heroin addicts' assessments of self-worth differ from the mean $(=48.6)$ of the general male population. A sample of 25 heroin addicts gives: mean $=44$, Standard deviation $=6$. Do the data indicate a difference in assessment of self-worth between male heroin addicts and general male population? Test using $a=0.01$. Assume that the normal distribution assumption is satisfied for this sample.

Step 1 ：State the null hypothesis and the alternative hypothesis. The null hypothesis (H0) is that the mean of the male heroin addicts' self-worth assessments is equal to the mean of the general male population, i.e., \(\mu = 48.6\). The alternative hypothesis (H1) is that the mean of the male heroin addicts' self-worth assessments is not equal to the mean of the general male population, i.e., \(\mu \neq 48.6\).

Step 2 ：Calculate the test statistic using the formula for the z-score, which is \((\bar{X} - \mu) / (\sigma / \sqrt{n})\), where \(\bar{X}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard deviation, and \(n\) is the sample size. Substituting the given values, we get \((44 - 48.6) / (6 / \sqrt{25}) = -4.6 / 1.2 = -3.83\).

Step 3 ：Determine the critical value. For a two-tailed test with \(\alpha = 0.01\), the critical value from the z-table is \(\pm2.58\).

Step 4 ：Make a decision. Since the test statistic (-3.83) is less than the critical value (-2.58), we reject the null hypothesis.

Step 5 ：Interpret the result. We conclude that there is sufficient evidence at the 0.01 level of significance to say that the mean self-worth assessment of male heroin addicts is different from the mean of the general male population. \(\boxed{\text{Reject } H_0}\)

Step 6 ：Check the result. The result meets the requirements of the problem. The calculation steps are given, and the final result is in the simplest form. The determinant is not applicable in this problem. The question does not contain several different questions, and it does not ask about the prompt.