The New York Times reported that "from 2001 to 2003, World Health Organization surveys measured the prevalence of serious mental disorders in the populations of various countries." A comparison was made between eight developed and seven less-developed countries.
a. Give at least one reason why we may suspect rate of mental illness to be higher in undeveloped countries, and give at least one reason why we may suspect it to be higher in developed countries.
b. Given that either of the circumstances in part (a) could be expected, formulate appropriate null and alternative hypotheses.
c. Use software to produce side-by-side boxplots of the two data sets, and tell which country is responsible for the outlier.
d. Carry out a two-sample t test, reporting the t statistic and the P-value.
e. Delete the outlier and carry out the test again, reporting the t statistic and the P-value.
f. To what extent did the outlier affect the size of t, the size of the P-value, and the test's conclusion?
g. The article mentions that "embarrassment about disclosing mental illness varies from country to country"; in some countries, like Nigeria, women are reluctant to admit being depressed. What, if anything, can we conclude about comparative rates of mental illness, based on the size of the P-value?