Heat treatment
As an engineer, you wish to know if a particular heat treatment increases the elastic modulus of aluminum. You cut multiple pieces of aluminum and measure the elastic modulus before the treatment ($X_{before}$) and after the treatment ($X_{after}$). The order of the measurements in $X_{before}$ is the same as in $X_{after}$.
$X_{before} = [40, 33, 38, 32, 24]$
$X_{after} = [43, 35, 36, 35, 27]$
Assume that the elastic moduli are normally distributed.
23-24. What are the appropriate null and alternative hypotheses?
Hypothesis
23. $H_0$
Choose...
24. $H_1$
Choose...
Statement
A. $\mu_{before} > \mu_{after}$
B. $\mu_{before} < \mu_{after}$
C. $\mu_{before} \ge \mu_{after}$
D. $\mu_{before} \le \mu_{after}$
25. What is the value of the test statistic? Round to the nearest hundredth.
26. What is the p-value? Round to the nearest hundredth. If you are using the tables, choose the p-value corresponding to the test statistic in the table that is closest to the test statistic you calculated.