Question

Many people believe that unusual behavior is more likely to occur during a full moon. As a test for empirical evidence to support this belief, suppose that you categorized the visits of new clients to a community health unit over a one-year period by lunar phases and found the following distribution of visits:

Full moon 62,

new moon 50,

first quarter 60,

third quarter 56.

Answer the following questions:

1. What are the null and alternate hypotheses?

2. What are the expected values for each of the categories?

3. What is the chi-square obtained?

4. What is the critical value?

5. What is your statistical decision? Justify your answer.

6. What is your conclusion?

Answer 1

ANSWER:

Given that,

1)

null hypotheses :

visits of new clients appear uniformly over a one-year period by lunar phases.

Alternate hypotheses:

visits of new clients do not appear uniformly over a one-year period by lunar phases.

2)

expected values for each of the categories =np=228*0.25 =57

3)

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Full moon	0.250	62.000	57.00	0.66	0.439
new moon	0.250	50.000	57.00	-0.93	0.860
First quarter	0.250	60.000	57.00	0.40	0.158
third quarter	0.250	56.000	57.00	-0.13	0.018
total	1.000	228	228		1.474

chi-square obtained =1.474

4)

for 0.05 level and 3 degree of freedom :crtical value =

7.815

5)

as test statistic is less than critical value we fail to reject null hypotheiss

6)

we do not have enough evidence at 0.05 level to conclude that visits of new clients do not appear uniformly over a one-year period by lunar phases.