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 table.

the researcher would like to test these hypotheses:

$h_0$: there is no difference in the distribution of responses among these three populations.

$h_a$: there is a difference in the distribution of responses among these three populations.

the conditions for inference are met. the chi - square test statistic is 0.19, df = 2, and the p - value is greater than any reasonable significance level. what conclusion should be made?

there is convincing evidence that the proportions of these students, parents, and teachers who volunteer at least once a month differs.

there is not convincing evidence that the proportion of these students, parents, and teachers who volunteer at least once a month differs.

there is convincing evidence that the distribution of responses for the population of all students, parents, and teachers of this large high school differs.

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.

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 table.

the researcher would like to test these hypotheses:

$h_0$: there is no difference in the distribution of responses among these three populations.

$h_a$: there is a difference in the distribution of responses among these three populations.

the conditions for inference are met. the chi - square test statistic is 0.19, df = 2, and the p - value is greater than any reasonable significance level. what conclusion should be made?

there is convincing evidence that the proportions of these students, parents, and teachers who volunteer at least once a month differs.

there is not convincing evidence that the proportion of these students, parents, and teachers who volunteer at least once a month differs.

there is convincing evidence that the distribution of responses for the population of all students, parents, and teachers of this large high school differs.

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.

Accepted Answer

# Brief Explanations:
When conducting a hypothesis test, if the $P -$value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis ($H_0$). Here, the $P -$value is greater than any reasonable significance level (commonly $\alpha = 0.01,0.05,0.1$). The null hypothesis $H_0$ states that there is no difference in the distribution of responses among the three populations (students, parents, teachers). Failing to reject $H_0$ means there is not enough evidence to support the alternative hypothesis ($H_a$) which claims a difference.

# Answer:
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.

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