Question

4. A psychologist is interested in whether young infants learn to recognize their own mothers' voices early in life, and whether their mothers' voices are more attractive to them than a stranger's voice. The psychologist presents 10 one-month-old infants with voices coming from different locations. Half of the time, the voice is the mother's; half the time, the voice is another female's voice. The psychologist measures how many times each infant turns toward each voice. 10 Subject ID #: Mother Stranger 1 9 6 2 3 4 | 10 | 10 | 5 9 7 | 4 5 | 6 | 6 6 | 6 7 7 8 | 9 | 10 | 6 | 5 9 8 | 7 6 a. Construct the 98% confidence interval to estimate the mean difference in the number of responses to mother's vs. stranger's voices. Compute the magnitude of the effect of the type of voice using Cohen's d. c. Summarize your findings in words.

Answer 1

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
9	6	3.000	1.440
10	9	1.000	0.640
10	7	3.000	1.440
5	4	1.000	0.640
6	6	0.000	3.240
6	7	-1.000	7.840
9	6	3.000	1.440
10	5	5.000	10.240
8	7	1.000	0.640
8	6	2.000	0.040

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	81	63	18.000	27.600

sample size ,    n =    10          
Degree of freedom, DF=   n - 1 =    9   and α =    0.02  
t-critical value =    t α/2,df =    2.8214   [excel function: =t.inv.2t(α/2,df) ]      
                  
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    1.7512          
                  
std error , SE = Sd / √n =    1.7512   / √   10   =   0.5538
margin of error, E = t*SE =    2.8214   *   0.5538   =   1.5624
                  
mean of difference ,    D̅ =   1.800          
confidence interval is                   
Interval Lower Limit= D̅ - E =   1.800   -   1.5624   =   0.238
Interval Upper Limit= D̅ + E =   1.800   +   1.5624   =   3.362
                  
so, confidence interval is (   0.2376   < µd <   3.3624   )  

b)

cohen's d = |Dbar/ std dev| =    1.03

c)

there is 98% confidence that there are more responses to mother as compare to stranger's voices

and this difference is large enough