In a study done in England Voss and Mulligan 2000 collected

In a study done in England, Voss and Mulligan (2000) collected data on height (short or not) and whether or not the student had ever been bullied in school for 209 secondary school students. A student was categorized as short if he or she was below the third percentile for height on school entry, but the researchers intentionally sampled in a way that made short students constitute almost half of the sample. The following table displays a contingency table of the data. Does the proportion 92/209 estimate the proportion of short students in the entire population? Why or why not? What is the proportion of short students in the entire population? For each height category, calculate the risk of having been bullied. What is the relative risk for short students of having been bullied (compared to not short students)? Write a sentence that interprets this relative risk. What is the percent increased risk of having been bullied for short students? Write a sentence that interprets this increased risk. Calculate the odds ratio that compares the odds of having been bullied for the short students to the odds for students who are not short. Write a sentence that interprets this ratio.

Solution

a) YES THE PROPORTION 92/209 ESTIMATES THE PROPORTION OF SHORT STUDENTS IN THE ENTIRE POPULATION

WHY? BECAUSE YOU ARE TAKING ALL OF THE PEOPLE WHO IS SHORT IN THIS STUDY

b)

having been bullied

shorts = 42 / 209 = 0.2009 = 20.09%

not shorts = 30 / 209 = 0.1435 = 14.35%

c)

short students of having been bullied = 0.2009 / [72/209] =0.5832= 58.32%

not short students of having been bullied = 0.1435 / [72/209] =0.4165 = 41.65%

d)

percent increased risk of having been bullied for short students

0.3445-0.2009 / 0.2009   = 0.7148 = 71.48%

e)

I can gladly help you but you should post it in a new question