Question

Some Alzheimer’s caregivers were asked to respond to the following statement: “Caregiving enabled me to develop a more positive attitude toward life.” The responses are reflected in the following table.

Strongly Disagree	Somewhat Disagree	No Opinion	Somewhat Agree	Strongly Agree
166	116	171	234	542

1. Graph the data. Based on your graph, is there evidence to suggest the distribution is not uniform?
2. Run a statistical test to see if the data indicate the true distribution is not uniform. State the hypotheses, obtain a p-value, and state your conclusion.

Answer 1

a)

from graph, data indicate the true distribution is not uniform

b)

Ho:  data indicate the true distribution is uniform

H1:  data indicate the true distribution is not uniform

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency  
total frequency=   1229

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
166	0.2000	245.800	-79.80	6368.04	25.907
116	0.2000	245.800	-129.80	16848.04	68.544
171	0.2000	245.800	-74.80	5595.04	22.763
234	0.2000	245.800	-11.80	139.24	0.566
542	0.200	245.800	296.20	87734.44	356.934

chi square test statistic,X² = Σ(O-E)²/E =   474.7144              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   5   -   1   =   4
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  

conclusion: there is enough evidence to conclude that data indicate the true distribution is not uniform