Mulvihill, Obuseh, and Caldwell (2008) conducted a survey evaluating healthcare
ID: 3174739 • Letter: M
Question
Mulvihill, Obuseh, and Caldwell (2008) conducted a survey evaluating healthcare providers’ perception of a new state children’s insurance program. One question asked the providers whether they viewed the reimbursement from the new insurance as higher, lower, or the same as private insurance. Another question assessed the providers’ overall satisfaction with the new insurance. The following table presents observed frequencies similar to the study results.
Opinion
Favor
Oppose
City
35
15
50
Suburb
55
45
100
90
60
Is there a significant difference in the distribution of opinions for city residents compared to those in the suburbs? Test at the .05 level of significance.
The relationship between home location and opinion can also be evaluated using the phi-coefficient. If the phi-coefficient were computed for these data, what value would be obtained for phi?
Favor
Oppose
City
35
15
50
Suburb
55
45
100
90
60
Explanation / Answer
Hypotheses: H0: opinion for city residents is independent of opinion of suburb.
H1: opinion for city residents and opinion for suburbs are not independent.
Asumptions: Counted data condition: There are counts of individuals classified in two categories.
Independence assumption: the people in this study are independent of each other.
Randomization condition: this is a survey, the samples might not be SRS, but it is assumed that they are selected in order to avoid bias.
10% condition: the total 150 people are far less than 10% of all those who have opinion and live in city or suburb.
Expected cell frequency: the expected cell frequency is atleast 5.
X^2=sigma (observed-expected)^2/expected
=3.125
p value at 1 df [df=(row-1)(column-1)=(2-1)(2-1)] is 0.077.
Conclusion: Rule says, reject H0, if p value is less than 0.05. Here, p value is not less than 0.05, therefore, fail to reject H0. There is insufficient sample evidence to conclude that opinion for city residents and opinion for suburbs are not independent.
phi-coefficient: sqrt (X^2/N)
=sqrt (3.125/150)
=0.14
Observed Expected, fe:[(column marginal*row marginal)/total] (observed-expected)^2/expected 35 30 [(50*90)/150] 0.8333 [(35-30)^2/30] 15 20 1.2500 55 60 0.4167 45 40 0.6250X^2=sigma (observed-expected)^2/expected
=3.125
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