Prove the hypothesis that the average content of containers of a particular lubricant is $10$ liters, if the contents of a random sample of $10$ containers are:
\begin{array}{|c|c|c|c|c|} \hline 10,2 & 9,7 & 10,1 & 10,3 & 10,1 \\\hline 9,8 & 9,9 & 10,4 & 10,3 & 9,8 \\\hline \end{array}
Use a significance level of $0.01$ and assume that content distribution is normal.
I started with the following:
In this case, use $t=\dfrac{\overline{x}-\mu_0}{s/\sqrt{n}}$, because I do not know anything about $\sigma$.
- $H_0: \mu= 10$.
- $H_1: \mu \neq 10$.
- $\alpha = 0,01$.
- How can I find the critical region?
- How I can decide if the hypothesis is correct?
Thank you very much.