Answer
No, see explanations.
Work Step by Step
Given $\sigma^2=3.81, n=15, s=2.08$
a. State the hypotheses and identify the claim.
$H_o: \sigma^2=3.81$
$H_a: \sigma^2\ne 3.81$ (claim, two tail test)
b. Find the critical value(s).
$\alpha/2=0.025, df=14, \chi^2_{left}=5.629, \chi^2_{left}=26.119$
c. Compute the test value.
$\chi^2=\frac{15\times2.08^2}{3.81}=17.03$
d. Make the decision.
The above value fall in the non-rejection region and we fail to reject the null hypothesis.
e. Summarize the results.
At α=0.05, there is not sufficient evidence to conclude a difference from the population variance.