Question

9Do unregulated providers of child care in their homes follow different health and safety practices in different cities? A study looked at people who regularly provided care for someone else's children in poor areas of three cities. The numbers who required medical releases from parents to allow medical care in an emergency were 42 of 73 providers in Newark, New Jersey, 29 of 101 in Camden, New Jersey, and 48 of 107 in South Chicago, Illinois. A)Use the chi-square test to see if there are significant differences among the proportions of child care providers who require medical releases in the three cities. What do you conclude? B)How should the data be produced in order for your test to be valid? (In fact, the samples came in part from asking parents who were subjects in another study who provided their childcare. The author of the study, wisely did not use a statistical test. He wrote: Application of conventional statistical procedures appropriate for random samples may produce biased and misleading results.

Answer 1

9Do unregulated providers of child care in their homes follow different health and safety practices in different cities? A study looked at people who regularly provided care for someone else's children in poor areas of three cities. The numbers who required medical releases from parents to allow medical care in an emergency were 42 of 73 providers in Newark, New Jersey, 29 of 101 in Camden, New Jersey, and 48 of 107 in South Chicago, Illinois.

A)Use the chi-square test to see if there are significant differences among the proportions of child care providers who require medical releases in the three cities. What do you conclude?

Ho: the proportions of child care providers who require medical releases in the three cities are same

H1: the proportions of child care providers who require medical releases in the three cities are different

Chi-Square Test
Observed Frequencies
	Column variable					Calculations
Row variable	C1	C2	C3	Total		fo-fe
R1	42	29	48	119		11.0854	-13.7722	2.6868
R2	31	72	59	162		-11.0854	13.7722	-2.6868
Total	73	101	107	281
Expected Frequencies
	Column variable
Row variable	C1	C2	C3	Total		(fo-fe)^2/fe
R1	30.9146	42.7722	45.3132	119		3.9750	4.4345	0.1593
R2	42.0854	58.2278	61.6868	162		2.9199	3.2575	0.1170
Total	73	101	107	281
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	14.8633
p-Value	0.0006
Reject the null hypothesis

Calculated chi square 14.863 > 5.991 the critical chi square at 0.05 level of significance. Ho is rejected.

We conclude that the proportions of child care providers who require medical releases in the three cities are different.

B)How should the data be produced in order for your test to be valid? (In fact, the samples came in part from asking parents who were subjects in another study who provided their childcare. The author of the study, wisely did not use a statistical test. He wrote: Application of conventional statistical procedures appropriate for random samples may produce biased and misleading results.

Since data are not selected randomly to each group, generalizing the result is questionable. The data should be independent of each other. The results may not be valid. We have to select the samples randomly from each cities.