A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population.On a test designed to measure self-worth, the mean for the general population is 48.6.The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively.

a) Do these data indicate the self-worth of heroin addicts is less than that of the general population? Test at a .05 level of significance.

b) With 95% confidence, estimate the mean test score for the heroin addicts.