Question

Twelve sets of identical twins were enrolled in a study to measure the effect of home environment on certain social attitudes. One twin in each set was randomly assigned to a foster environment or a home environment. The twin assigned to the foster environment went to live with a low income family on state welfare for a period of 1 year. At the end of the year, an attitudinal survey was administered.  

Their results follow.

Twelve sets of identical twins were enrolled in a study to measure the effect of home environment on certain social attitudes. One twin in each set was randomly assigned to a foster environment or a home environment. The twin assigned to the foster environment went to live with a low income family on state welfare for a period of 1 year. At the end of the year, an attitudinal survey was administered.  

Their results follow.

Foster: 83   75   72    76   78   80  72   81   70   78   77 71   

Home: 65 67   75 77 69 65   73   78   70   72 73 79  

1- Test Statistic (state your answer accurate to 2 decimal places) t =

2-   State the Degrees of Freedom? df =

3- Look up the critical value t_c   (state to 3dp as given in your t-tables) t_c =

4- (reject/do not reject) Ho. There is (sufficient/insufficient)  living in the foster environment leads to higher scores on the attitudinal survey

Answer 1

We frame the null hypothesis

: Living in the foster environment leads to higher scores on the attitudinal survey.

To test the we use the Paired t - test ( Since the data related to dependent case )

Where

d = Difference between X and Y

n = Number of pairs of observations = 12

Wher X = Foster

Y = Home

X	Y	d = X - Y
83	65	18	13.8333	191.3611
75	67	8	3.8333	14.6944
72	75	-3	-7.1667	51.3611
76	77	-1	-5.1667	26.6944
78	69	9	4.8333	23.3611
80	65	15	10.8333	117.3611
72	73	-1	-5.1667	26.6944
81	78	3	-1.1667	1.3611
70	70	0	-4.1667	17.3611
78	72	6	1.8333	3.3611
77	73	4	-0.1667	0.0278
71	79	-8	-12.1667	148.0278
	TOTAL	50		621.6667
	MEAN	4.1667

Therefore  

Therefore

(2) The given Sample Size = n = 12

The degrees of freedom = (n - 1) = (12 - 1) = 11

(3) Critical Value of t

Since the Level of Significance is not specified; so, we took it as 5% i.e

(4) Since So, we Accept at 5% Level of Significant.

Therefore We conclude that "Living in the foster environment leads to higher scores on the attitudinal survey".

NOTE: The critical value of t has been extracted from the tabulated value of t; which is posted below.