The Journal of the American Medical Association reported that 215 male physician
ID: 3150318 • Letter: T
Question
The Journal of the American Medical Association reported that 215 male physicians who were Harvard Graduates and died between Nov 1974 and Oct 1977, the 125 in full-time practice lived an average of 48.9 years beyond graduation with a standard deviation of 14.6 years, while the 90 with the academic affiliations lived an average of 43.2 years beyond graduation with a standard deviation of 14.4 years. One is interested in testing whether mean life time after graduation for doctors in full-time practice exceeds the mean life time for those who obtain academic affiliation at 1% level of significance.
(a) State the hypotheses.
(b) Calculate the test statistic and the critical value.
(c) What do you conclude about the mean life time beyond graduation for the groups?
(d) What is the p-value of the test?
(e) Is this study a designed experiment or an observational study? Explain your answer.
(f) In view of your answers to parts (c) and (e), could you reasonably conclude that academic affiliation decreases the life time after graduation for doctors in academia.
Explanation / Answer
a) H0:mufp-muaa=0 (difference in mean life time for for doctors after graduation in full time practice is same as that of doctors after graduation who obtain academin affiliation)
H1: mufp-muaa>0 (difference in mean life time for for doctors after graduation in full time practice is more than that of doctors after graduation who obtain academin affiliation)
b)
For independent groups,
SE(xbarft-xbaraa)=sqrt [s^2ft/nft+s^2aa/naa]=sqrt[14.6^2/125+14.4^/90]=2
t=[( xbarft-xbaraa)-0]/SE(xbarft-xbaraa)=(48.9-43.2)/2=2.85
For df=193, at alpha=0.01, the critical t value is 2.35.
c) The test statistic falls in critical region, therefore, reject null hypothesis. There is sufficient evidence to conclude that mena life time for doctors after graduation in full practice is more than mean life of doctors obtaining academic affiliation after graduation.
d) Using technology, the exact p value is 0.005.
e) The study is experimental one , where independent group assumption, randomization condition and independence assumption is followed.
f) This can not be ascertained from the study, as the purpose of the study was to comapre mean life time of doctors after graduation in full time practice and academia.
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