What is the effect of going through a natural disaster on the attitude of police chiefs about the goodness of the people in their city? A researcher studying this expects a more positive attitude (because of the many acts of heroism and helping of neighbors), but a more negative attitude is also possible (because of looting and scams). It is known that, using a 1-to-10 scale (from 1 = extremely negative attitude to 10 = extremely positive attitude), in general police chiefs' attitudes about the goodness of the people in their cities is normally distributed, with a mean of 6.5 and a standard deviation of 2.1. A major earthquake has just occurred in an isolated city, and shortly afterward the researcher is able to give the attitude questionnaire to the police chief of that city. The chief's score is 8.2.
(a) Using the .05 significance level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.
(b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).