In 2003, the American Psychological Association conducted a survey (at research.apa.org) of a random sample of psychologists to estimate mean incomes for psychologists with various academic degrees and levels of experience. Of the 31 psychologists who received a master’s degree in 2003, the mean income was $43,834 with a standard deviation of $16,870.
a. Construct a 95% confidence interval for the population mean. Interpret.
b. What assumption about the population distribution of psychologists’ incomes does the confidence interval method make?
c. If the assumption about the shape of the population distribution is not valid, does this invalidate the results? Explain.