Question

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: volunteer?

student	parent	teacher
no	21	13	6

expected counts: volunteer?

student	parent	teacher
no	21.95	12.20	5.85

the researcher would like to test these hypotheses: ( h_0 ): there is no difference in the distribution of because the ( p )-value of this test is large, there is not convincing evidence that the distribution of responses for the population of all students, parents, and teachers of this large high school differs. for which categories are the observed counts greater than expected?
there were more students than expected who do not volunteer, and more parents and teachers than expected who do volunteer.
there were more students than expected who do volunteer, and more parents and teachers than expected who do not volunteer.
there were more teachers than expected who do not volunteer, and more students and parents than expected who do volunteer.
there were more teachers than expected who do volunteer, and more students and parents than expected who do not volunteer.

Explanation:

Compare the observed and expected counts. For students: Observed yes \(24>23.05\) (expected yes), observed no \(21 < 21.95\) (expected no). For parents: Observed yes \(12<12.80\) (expected yes), observed no \(13>12.20\) (expected no). For teachers: Observed yes \(6<6.15\) (expected yes), observed no \(6>5.85\) (expected no).

Answer:

There were more students than expected who do volunteer, and more parents and teachers than expected who do not volunteer.