Answer
a. $\sigma =1.8 ; \sigma \lt 1.8$
b. .694
c. We should reject it.
d. We should accept it.
e. It is effective.
Work Step by Step
a. The null hypothesis is the original situation, which is $\sigma =1.8$. The alternative hypothesis is $\sigma \lt 1.8$, for this is what we want to verify.
b. We find that the test statistic equals:
$=\frac{(n-1)(s^2)}{\sigma^2}=.694$
c. Since this value is less than .05, we see that we should reject the null hypothesis.
d. Since we rejected the null hypothesis, it follows that we should accept the alternative hypothesis, which is the original claim.
e. Since we accepted the alternative hypothesis, we see that the change actually did help.
