Answer
Yes, see explanations.
Work Step by Step
Given $\sigma=4.3, n=20, s=2.6$
a. State the hypotheses and identify the claim.
$H_o: \sigma\geq 4.3$
$H_a: \sigma\lt 4.3$ (claim, left tail test)
b. Find the critical value(s).
$ \alpha=0.05$
c. Compute the test value.
$\chi^2=\frac{19\times2.6^2}{4.3^2}=6.95, df=19, P=1-0.994=0.006$ (area to the left the $\chi^2$)
d. Make the decision.
$P\lt \alpha$, it is in the rejection region and we should reject the null hypothesis.
e. Summarize the results.
Under the conditions given, the standard deviation is really less than previously thought.
