The margin of error (E) can be calculated using the formula:
E = t_(α/2) * (s/√n)
Where t_(α/2) is the critical value of the t-distribution with (n-1) degrees of freedom at the desired level of confidence (α/2), s is the sample standard deviation, and n is the sample size.
At a 95% confidence level, the value of α/2 is 0.025. Using a t-distribution table or calculator with (n-1) = 21 degrees of freedom, we find that the critical value is approximately 2.08.
Substituting the given values into the formula, we get:
E = 2.08 * (10/√22)
E ≈ 4.38
Therefore, the margin of error at a 95% confidence level is approximately 4.38.