Ap Statistics-Adams Chapter 10 Review With Answers - Woodstown-Pilesgrove Regional School District Page 4
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10. A sociology class is interested in knowing whether there is a relationship between personality
style and type of extracurricular activity. The class took a random sample of 200 students
from a large high school and recorded these data.
Personality Style
Extrovert
Normal
Introvert
Sports
21
44
25
Type of
Extracurricular
Club
16
33
20
Activity
None
3
16
22
Using the standard four-step process (name test and check conditions; state hypotheses;
compute test statistic and P-value and draw a sketch; and write a conclusion in context), test
the null hypothesis that personality style and type of extracurricular activity are independent.
Name the test. Chi-square test of independence.
Check conditions. A random sample was taken from one large population. Each outcome can be
classified into one of three categories for each of the two variables. The expected number in each cell is
at least 5. The table of expected counts is shown here.
Personality Style
Extrovert Normal Introvert
Sports
18
41.85
30.15
Type of
Extracurricular
Club
13.8
32.085
23.115
Activity
None
8.2
19.065
13.735
State your hypotheses.
H
: Personality style and activity type are independent in the population of all students in this high
0
school.
H
: Personality style and activity type are not independent.
a
Compute the test statistic and P-value and draw a sketch.
−
2
(
O E
)
∑
χ
=
≈
2
11.05
E
≈
P
-value
0.026
; 4 degrees of freedom
Write a conclusion in context. Because the P-value of 0.026 is less than 0.05, the null hypothesis that
the two variables are independent can be rejected. In other words, there is evidence that there is an
association between personality style and activity type.
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