Question

Internet addiction has been described as excessive and uncontrolled Internet use. The authors of a research article used a score designed to measure the extent and severity of Internet addiction in a study of 832 male and 872 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 1.59 and the standard deviation was 2.09. For the sample of females, the mean was 1.02 and the standard deviation was 1.67. 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. 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. (Round your numeric values to two decimal place.) If the distributions were both approximately normal, then ____% of the male Internet Addiction scores would be negative, and ___% of the female Internet Addiction scores would be negative. Assuming that the scores must be positive, these percentages are too large to make it reasonable to believe that the distributions are approximately normal.

Answer 1

The Internet Addiction scores for sixth-grade students in China do not follow a normal distribution as the mean is less than the standard deviation for both males and females and the assumption of normality would imply a significant proportion of impossible negative scores.

Step-by-step explanation:

When analyzing the Internet Addiction scores for male and female sixth-grade students in China using Young's Internet Addiction Diagnostic Test, the distribution of scores is pivotal to draw inferences about the population. If the mean score is lower than the standard deviation, as is the case for both males (mean=1.59, SD=2.09) and females (mean=1.02, SD=1.67), expecting a normal distribution is problematic. In a normal distribution, about 68% of values lie within one standard deviation of the mean, implying many scores would fall below zero, which isn't possible for these scores as they must be positive. Hence, it is likely that the distribution is skewed, and a large number of students have low Internet addiction scores, with fewer students having higher scores, illustrating that the scores are not spread symmetrically around the mean.

For a normal distribution, approximately 16% of scores would lie beyond one standard deviation below the mean (below -0.50 for males, and below -0.65 for females). However, given that Internet Addiction scores cannot be negative, these would incorrectly indicate a proportion of negative scores, which is impossible and thus too large to support the assumption of normality. Negative scores on a test that measures quantities that cannot be negative suggest a left-skewed distribution rather than a normal distribution. Therefore, we can conclude that the distribution of Internet Addiction scores is not normal for either the populations of male or female Chinese sixth-grade students.