Question

Scores on the Cognitive Scale of the Bayley-Scales of Infant and Toddler Development range from 1 to 19, with a standard deviation of 3. Calculate the margin of error in estimating the true mean cognitive scale score, with 99% confidence, if there are 12 infants and toddlers in a sample.

Answer 1

Answer: 2.693

Explanation:

The formula to calculate the margin of error ( for small sample ) is given by :-

`E= t_(\alpha/2, n-1)(\sigma)/(√(n))`

Given : Significance level :
`\alpha: 1-0.99=0.01`

Standard deviation =
`\sigma=3`

Sample size = 12 <30 , so we use t-test.

Critical value :
`t_(n-1,\alpha/2)=t_(11,0.005)=3.1096`

Then, the margin of error will be :-

`E= (3.1096)(3)/(√(12))\\\\=2.69299259561\approx2.693` [Rounded to the nearest three decimal places.]

Hence, the margin of error in estimating the true mean cognitive scale score : 2.693