The goal of a nutritional study was to compare the caloric intake of adolescents living in rural areas of the US with the caloric intake of those living in urban areas. A random sample of ninth-grade students from one high school in a rural area was selected. Another random sample of ninth graders from one high school in an urban area was selected. Each student in the sample kept records of all the food he or she consumed in one day. The back to back stemplot displays the number of calories of food consumed per kilogram of body weight for each student on that day.
a. Write a few sentences comparing the distribution of the daily caloric intake of 9th-grade students in one rural high school with the distribution of the daily caloric intake of 9th-grade students in the urban high school.
b. Is it reasonable to generalize the findings of this study to all rural and urban 9th-grade students in the US?

To give more clarity to the question, lets examine the attached back-to-back stem plot.

A)

Having examined the stem plot, we can using quick calculations, summarize that:

The mean (40.45 cal/kg) and median (41 cal/kg) daily caloric intake of ninth-grade students in the rural school is higher than the corresponding measures of center, mean (32.6 cal/kg) and median (32 cal/kg), for ninth-graders in the urban school.

The median and the mean for the students in the 9th grade in the urban school is lower than that of those of their contemporaries in the rural school. The respective medians and means are stated below:

Urban 9th Grade Students

Median = 32 cal/kg

Mean = 36 cal/kg

Rural 9th Grade Students

Median = 41 cal/kg

Mean = 41 cal/kg

Please note that all figures above have been approximated to the nearest whole number.

B)

It is unreasonable to generalize the findings of this study to all rural and urban 9th-grade students in the United States because the sample is too small compared to the target population size.

To allow for generalization, they would have to collect and analyze more samples say from every state within America.

Cheers!