Answer: 2.693
Step-by-step explanation:
The formula to calculate the margin of error ( for small sample ) is given by :-
[tex]E= t_{\alpha/2, n-1}\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Significance level : [tex]\alpha: 1-0.99=0.01[/tex]
Standard deviation = [tex]\sigma=3[/tex]
Sample size = 12 <30 , so we use t-test.
Critical value : [tex]t_{n-1,\alpha/2}=t_{11,0.005}=3.1096[/tex]
Then, the margin of error will be :-
[tex]E= (3.1096)\dfrac{3}{\sqrt{12}}\\\\=2.69299259561\approx2.693[/tex] [Rounded to the nearest three decimal places.]
Hence, the margin of error in estimating the true mean cognitive scale score : 2.693
