Question

A study was conducted to determine the effect of early child care on infant-mother attachment patterns. In the study, 102 infants were classified as either ``secure'' or ``anxious'' using the Ainsworth strange situation paradigm. In addition, the infants were classified according to the average number of hours per week that they spent in child care. The data are presented in the table:

	Low (0-3 hours)	Moderate (4-19 hours)	High (20-54 hours)
Secure	25	34	8
Anxious	10	12	13

H0: Attachment and Time Spent in Child Care are IndependentDoes the data provide sufficient evidence to indicate that there is a difference in attachment pattern for the infants depending on the amount of time spent in child care? Test the hypotheses

HA:Attachment and Time Spent in Child Care are Dependent

using α=0.05.

For ν= degrees of freedom we have χ20.05=  

Answer 1

Hypothesis :

H₀ : Attachment and Time Spent in Child Care are Independent

H_{1 :} Attachment and Time Spent in Child Care are Dependent

Critical value :

Significance level = = 0.05

Degrees of freedom = ( r - 1 ) ( c - 1 ) = ( 2 - 1 )(3 -1 ) = 2

{ Where , r number of row , c number of column }

So chi-square critical value for this test is,

                   { Using Excel, =CHIINV( 0.05 , 2 ) = 5.9915 }

Rejection region : { : > 5.9915 }

Test statistic :

Where , O is observed frequency

E is expected frequency

Where , Ri is total of i^th row.

Cj is total of j^th column

Calculation :

Given observed frequency table ,

Expected frequencies.

Based on the observed and expected values, the squared distances can be computed according to the following formula: ( O - E )^2 / E

Chi-square test statistic is ,

Decision about null hypothesis :

Rejection region : { : > 5.9915 }

It is observed that , test statistic ( 8.956 ) is greater than critical value ( 5.9915 )

So reject null hypothesis .

Conclusion :

The data provide sufficient evidence to conclude that Attachment and Time Spent in Child Care are Dependent.