An experiment was conducted to compare two methods for operating a group family

Question

An experiment was conducted to compare two methods for operating a group family

medical practice. Four hundred patients were randomly assigned to two groups: one group

received the conventional direct contact with physicians, while the other group made first contact

with a nurse-practitioner and were then referred to a physician if a physician's services were

deemed necessary. At the conclusion of the experiment, the quality of each person's medical

care was rated as satisfactory by an impartial medical observer in consultation with the patient.

The results of the experiment are shown in the table. Do the data present sufficient evidence to

indicate a difference in the proportions of satisfactory ratings for the two methods of patient care?

Test using interval=0.05.

Results

First Contact Satisfactory Unsatisfactory Totals

Conventional 146 54 200

Nurse Practitioner 159 41 200

Explanation / Answer

Null hypothesis -> H0 : satisfactory ratings of two methods are independent of each other.
Alternative hypothesis -> H1 : not H0.

R CODES:
> tab=matrix(c(146,54,159,41),nrow=2,byrow=T)
> rownames(tab)=c("Conventional","Nurse")
> colnames(tab)=c("Satisfactory","Unsatisfactory")
> tab
Satisfactory Unsatisfactory
Conventional 146 54
Nurse 159 41
> chisq.test(tab) #CHI-SQUARE TEST OF INDEPENDENCE

Pearson's Chi-squared test with Yates' continuity correction

data: tab
X-squared = 1.9879, df = 1, p-value = 0.1586

Since p-value > 0.05, we accept the null hypothesis of independence between satisfaction and method type and conclude that there is no significant difference in proportions of satisfactory ratings between the two methods.

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