Question

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is:

Do these data indicate that gum disease is equally likely regardless of smoking status?

Using a significance level of 0.05, what is the appropriate conclusion for this test?

The data are consistent with an equal representation of current, former, and never smokers among adults diagnosed with gum disease.

Current smokers make up a significantly greater proportion of adults diagnosed with gum disease than former or never smokers.

Current smokers are most likely to have gum disease.

There is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.

Answer 1

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency  
total frequency=   4048

observed frequencey, O	expected proportion	expected frequency,E	(fi - ei)		(O-E)²/E
2226	0.333	1349.333	876.667		569.573
891	0.333	1349.333	-458.333		155.684
931	0.333	1349.333	-418.333		129.696

chi square test statistic,X² = Σ(O-E)²/E =   854.9531              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   3   -   1   =   2
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  

There is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.