Internet addiction has been described as excessive and uncontrolled Internet use. The authors of the paper “Gender Difference in the Relationship Between Internet Addiction and Depression” (Computers in Human Behavior [2016]: 463–470) used a score designed to measure the extent and severity of Internet addiction in a study of 836 male and 879 female sixth-grade students in China. Internet addiction was measured using Young’s Internet Addiction Diagnostic Test. The lowest possible score on this test is zero, and higher scores indicate higher levels of Internet addiction. For the sample of males, the mean Internet Addiction score was 1.51 and the standard deviation was 2.03. For the sample of females, the mean was 1.07 and the standard deviation was 1.63. For purposes of this exercise, you can assume that it is reasonable to regard these two samples as representative of the population of male Chinese sixth-grade students and the population of female Chinese sixth-grade students, respectively.

a. The standard deviation is greater than the mean for each of these samples. Explain why it is not reasonable to think that the distribution of Internet Addiction scores would be approximately normal for either the population of male Chinese sixth-grade students or the population of female Chinese sixth-grade students.

b. Given your response to Part (a), would it be appropriate to use the two-sample t test to test the null hypothesis that there is no difference in the mean Internet Addiction score for male Chinese sixth-grade students and female Chinese sixth-grade students? Explain why or why not.

c. If appropriate, carry out a test to determine if there is convincing evidence that the mean Internet Addiction score is greater for male Chinese sixth-grade students than for female Chinese sixth-grade students. Use α = 0.05.