A survey is conducted to determine if there is a difference in the proportion of students, parents, and teachers who volunteer at least once a month. To investigate, a random sample of 45 students, 25 parents, and 12 teachers was selected from a large high school. The data are displayed in the tables. Observed counts:   Expected counts:   The researcher would like to test thes

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A survey is conducted to determine if there is a difference in the proportion of students, parents, and teachers who volunteer at least once a month. To investigate, a random sample of 45 students, 25 parents, and 12 teachers was selected from a large high school. The data are displayed in the tables.

Observed counts:

 

Expected counts:

 

The researcher would like to test these hypotheses:

H0: There is no difference in the distribution of responses among these three populations.
Ha: There is a difference in the distribution of responses among these three populations.

The conditions for inference are met. What is the value of the chi-square test statistic and what are the degrees of freedom for this test?

χ‑2 = 0.19, df = 2
χ‑2 = 0.19, df = 5
χ‑2 = 0.44, df = 2
χ‑2 = 0.44, df = 5

Student
Parent
Teacher
Yes
23.05
12.80
6.15
Volunteer?
No
21.95
12.20
5.85
Transcribed Image Text:Student Parent Teacher Yes 23.05 12.80 6.15 Volunteer? No 21.95 12.20 5.85
Student
Parent
Teacher
Yes
24
12
Volunteer?
No
21
13
6
Transcribed Image Text:Student Parent Teacher Yes 24 12 Volunteer? No 21 13 6
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