Question: The revised version of the Minnesota Multiphasic Personality Inventory (MMPI-2) is the most frequently administered self-report personality measure. Test-takers respond to more than 500 true/false statements, and their responses are scored, typically by a computer, on a number of scales (e.g., hypochondriasis, depression, psychopathic deviation). Respondents receive a T score on each scale that can be compared to norms. (It is im portant to note that T scores are different from the t statistic we will learn about in a few chapters; you're likely to encounter T scores if you take psychology classes, and it's good to be aware that they're different from the t statistic.) T scores are another way to standardize scores so that percentiles and cutoffs can be determined. The mean T score is always 50, and the standard deviation is always 10. Imagine that you administer the MMPI-2 to 95 respondents who have recently lost a parent; you wonder whether their scores on the depression scale will be, on average, higher than the norms. You find a mean score on the depression scale of 55 in your sample.
a. Using symbolic notation, report the mean and standard deviation of the population.
b. Using symbolic notation and formulas (where appropriate), report the mean and standard error for the distribution of means to which your sample will be compared.
c. In your own words, explain why it makes sense that the standard error is smaller than the standard deviation.