(Solved): A certain pen has been designed so that true average writing lifetime under controlled conditions ( ...

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least $10\mathrm{hr}$. A random sample of 19 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample $t$ test. The relevant hypotheses are $H_0:\mu =10$ versus $H_a:\mu <10$. (a) If $t=-2.3$ and $\alpha =.05$ is selected, what conclusion is appropriate? Reject Fail to reject (b) If $t=-1.53$ and $\alpha =.01$ is selected, what conclusion is appropriate? Reject Fail to reject (c) If $t=0.57$, what conclusion is appropriate? Reject Fail to reject You may need to use the appropriate table in Appendix A to answer this question.