Question

1. the school attendance clerk is investigating the number of absences among teachers and students at a very large high school. she randomly samples 100 teachers and 600 students and records the number of days absent they had the previous semester. the results are shown in the table and segmented bar graph.

role
number of days absent student teacher
0 - 2 205 39
3 - 5 349 57
6+ 46 4

a. which variable is the explanatory variable? explain.
b. what proportion of the total sample had 5 or fewer absences?
\\(\frac{13}{14}\\)
c. what proportion of the students had 6+ absences?
d. what proportion of the teachers had 6+ absences?
\\(\frac{1}{25}\\)
e. is there an association between the role of the person and the number of days absent? explain.

Explanation:

Step1: Identify explanatory variable

The role (student or teacher) likely influences absences, so role is the explanatory variable.

Step2: Calculate proportion with 5 or fewer absences

Total number of people = 100 (teachers)+600 (students)=700.
Number of people with 5 or fewer absences = 205 + 349+39 + 57=650.
Proportion = $\frac{650}{700}=\frac{13}{14}$.

Step3: Calculate proportion of students with 6+ absences

Number of students = 600.
Number of students with 6+ absences = 46.
Proportion = $\frac{46}{600}=\frac{23}{300}$.

Step4: Calculate proportion of teachers with 6+ absences

Number of teachers = 100.
Number of teachers with 6+ absences = 4.
Proportion = $\frac{4}{100}=\frac{1}{25}$.

Step5: Check for association

The proportions of absences differ between students and teachers. For example, a much higher proportion of students have 3 - 5 absences compared to teachers. So, there is an association.

Answer:

a. The explanatory variable is the role (student or teacher) because the role is likely to influence the number of days absent.
b. $\frac{13}{14}$
c. $\frac{23}{300}$
d. $\frac{1}{25}$
e. Yes, there is an association. The proportions of absences in different absence - range categories differ between students and teachers.