Rock specimens are excavated from a particular geological formation and are subjected to a chemical analysis to determine their percentage content of cadmium. After analyzing $25$ specimens, the mean and the standard deviation are found to be $10.2$ and $3.1$, respectively. Suppose that a commercial extraction of this mineral will be economically feasible if the mean percentage content is at least $8$.
Do the data strongly support the feasibility of commercial extraction? (Test at $\alpha = .01$)
Attempted Solution:
Since $n < 30$, I will perform a t-test. The test statistic at $\alpha = .01$ with $df$ = $24$ gives $t$ = $2.4922$. We have,
$\frac{10.2-8}{3.1/5}$ = $3.55$. Since $3.55 > 2.4922$, the data strongly supports the feasibility of commercial extraction at $\alpha = .01$.
Did I do this correctly?
It's correct if you assume that the data is normally distributed. Otherwise you can use a a Wilcoxon test.