Question

Researchers have hypothesized that the distribution of the weight categories (underweight, normal, overweight\obese) of high school boys is changing over time. In 2006, the proportion of a large sample of high school boys was collected in 2006, resulting in the following proportions (Table 1):

Table 1: Distribution of weights of high school boys 2006

Weight classification (BMI range)	Proportion of high school boys
Underweight (<18 kg/m2)	4.8%
Normal weight (18-25 kg/m2)	80.4%
Overweight/obese (>25 kg/m2)	14.7%

In 2017, researchers classified 386 high school boys into the same categories and found the following counts (table2):

Table 2.  Distribution of weight of high school boys 2017 (counts)

Weight classification (BMI range)	Number of high school boys
Underweight (<18 kg/m2)	122
Normal weight (18-25 kg/m2)	69
Overweight/obese (>25 kg/m2)	195

What test would be used to assess if the distribution of weight of high school boys was the same in 2017 as it was in 2006?  Perform the test, stating the hypotheses, reporting the test statistic and p-value and interpret your result.

Answer 1

Here

We are using Chi square goodness of fit test to assess if the distribution of weight of high school boys was the same in 2017 as it was in 2006.

Null hypothesis , H0 : The weight of high school boys in 2017 is same as it was in 2006

Alternate hypothesis, H1 : The weight of high school boys in 2017 is not same as it was in 2006