Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease....

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Researchers selected a simple random sample of 4048 medicalrecords of adults diagnosed with gum disease. In all, 2226 werecurrent smokers, 891 were former smokers, and 931 never smokedregularly. Their research question is:

Do these data indicate that gum disease is equally likelyregardless of smoking status?
Using a significance level of 0.05, what is the appropriateconclusion for this test?
The data are consistent with an equal representation of current,former, and never smokers among adults diagnosed with gumdisease.
Current smokers make up a significantly greater proportion ofadults 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 neversmokers are not equally represented among adults diagnosed with gumdisease.

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3.5 Ratings (269 Votes)

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

observed frequencey, O	expected proportion	expected frequency,E	(fi - ei)	(O-E)Â²/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,XÂ² = Î£(O-E)Â²/E =Â Â 854.9531Â Â Â Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â
level of significance, Î±=Â Â 0.05Â Â Â Â Â Â Â Â Â Â Â
Degree of freedom=k-1=Â Â 3Â Â -Â Â 1Â Â =Â Â 2
Â Â Â Â Â Â Â Â Â Â Â Â Â Â
P value =Â Â 0.0000Â Â [ excel function: =chisq.dist.rt(test-stat,df) ]Â Â Â Â Â Â Â Â
Decision: P value < Î±, Reject HoÂ Â Â Â Â Â Â Â Â Â Â Â Â Â

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

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