Consider table below on the summary of patient satisfaction ratings on survey it

Question

Consider table below on the summary of patient satisfaction ratings on survey items related to timeliness of operations. Suppose the percentages are based on a response from a total of 200 patients. Regarding the item on timeliness of nurse visits, can we conclude that the proportion of responses in each rating category are equal? Use a significance level of 5%.

Table 5-15 Patient Satisfaction Data on Timeliness of Operations Rating Items 1.Waiting time at registration 2.Time to occupy bed 3.Waiting time prior to being seen by a physician 10 5 10 40 35 4.Timeliness of nurse visits 5.Waiting time to be checked out 10 40 20 20 10 10 30 30 20 10 30 20 20 20 10 20 30 10 30 10

Explanation / Answer

observed calculated out of each rating=200*column total/500

expected value for each rating=200/5=40

here we use chi-square test and

null hypothesis H0:all proportion are equal

alternate hypothesis: not all proportion are equal (at least two)

chi-square=sum((O-E)2/E) with (k-1) df

chi-squre=10.6 with (5-1)=4 df

critical chi-square(0.05,4)=9.49 is less than calculated chi-square 10.6, so we reject H0 and conclude that propotion of each rating category are not equal

rating items 1 2 3 4 5 total 1 10 40 20 20 10 100 2 10 30 30 20 10 100 3 10 5 10 40 35 100 4 30 20 20 20 10 100 5 20 30 10 30 10 100 total 80 125 90 130 75 500 observed(O) 32 50 36 52 30 200 Expected(E) 40 40 40 40 40 200 (O-E) -8 10 -4 12 -10 0 (O-E)2/E 1.6 2.5 0.4 3.6 2.5 10.6

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