Question

A researcher is interested in examining whether there are differences in students’ sense of safety across schools. She selects three schools and surveys five students from each school. The tab labeled Question 3 reflects the answers from this survey—the higher the score, the safer the student feels. Is there a difference between these schools in the students’ sense of safety?

School A	School B	School C
3	2	4
3	2	4
3	2	3
4	1	4
4	3	3

a. What is the null hypothesis?

b. What is the research hypothesis?

c. Why run an ANOVA statistical test?

d. What are the results of the hypothesis test? Interpret your findings. Can you reject the null hypothesis?

Answer 1

(a)

H0: Null Hypothesis: ( There are no differences in students’ sense of safety across schools)

(b)

HA: Alternative Hypothesis: (At least one mean is different from other 2 means) ( There are differences in students’ sense of safety across schools) (Claim)

(c) We run an ANOVA statistical test because here we are interested in determining whether there are any statistically significant difference between 3 independent groups.

(d)

From the given data, the following Table is calculated:

	School A	School B	School C	Total
N	5	5	5	15
	17	10	18	45
Mean	17/5=3.4	10/5=2	18/5=3.6	45/15=3
	59	22	66	147
Std. Dev.	0.5477	0.7071	0.5477	0.9258

From the above Table, ANOVA Table is calculated as follows:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between treatments	7.6	2	7.6/2=3.8	F=3.8/0.3667=10.3636
Within treatments	4.4	12	4.4/12=0.3667
Total	12	14

F=3.8/0.3667=10.3636

Degrees of Freedom for numerator = 2

Degrees of Freedom for denominator = 12

By Technology, P - Value = 0.0024

Since P - Value = 0.0024 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there are differences in students’ sense of safety across schools) .