Question

16.4 Two scholars are locked in debate regarding the interpretation of the accompanying data. One insists that the relationship between the age of a child and the child’s perception of the parents is very strong; the other argues that no relationship exists. Why do the two scholars reach different conclusions? Analyze the table and resolve the dilemma. Is there a relationship between the age of a child and the child’s perception of the parents?

	Age of Child (Years)
Child’s Perception of Parents	5–15	16–27
Negative	11%	53%
Neutral	18%	27%
Positive	71%	20%
Total	100%	100%

Answer 1

let us consider null and alternative hypothesis

Ho: there is no relationship between the age of a child and the child’s perception of the parents.

Ha:there a relationship between the age of a child and the child’s perception of the parents.

Chi-Square Test
Observed Frequencies
	age of child			Calculations
child's perception of parents	5 to 15	16 to 27	Total		fo-fe
negative	11	53	64		-21	21
neutral	18	27	45		-4.5	4.5
positive	71	20	91		25.5	-25.5
Total	100	100	200
Expected Frequencies
	age of child
child's perception of parents	5 to 15	16 to 27	Total		(fo-fe)^2/fe
negative	32	32	64		13.78125	13.78125
neutral	22.5	22.5	45		0.9	0.9
positive	45.5	45.5	91		14.29121	14.29121
Total	100	100	200
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	57.94492
p-Value	2.61E-13
Reject the null hypothesis

the value of chi-square test is 57.94492

the p-value of chi-square test is 0.0000

since p value is very small so we reject H0 and conclude that chi square test