Is p-value based on CLT? Please advise if CLT is related to p-value calculation.
Suppose there is a Hard Disk Drive (HDD) type 0 called $H_0$. The MTTF (Mean Time to Failure) data has been collected and its mean $\mu=2.97$.
Then, run random sampling (sample size 100) from $H_0$.

*

*Take 100 samples and calculate the sample mean $\overline{\mu}$ of MTTF.

*Repeat the step 1 many many times.

*Plot the histogram of the $\overline{\mu}$
According to CLT, $\overline{\mu}$ will form a normal distribution $ND$ with the mean $\mu=2.97$.
Question
Can p-value be calculated from the normal distribution $ND$ from the sampling above? For instance, to get p-value for $(MTTF>=4.29)$, use the cdf function of a normal distribution and calculate the size of the area on the right of $4.97$?
If it can be calculated, then can I say p-value is based on CLT?


No, the p-value is the probability of getting an effect as or more extreme than that observed in your sample, in datasets generated under the identical design and sampling scheme used for your study, when there is no effect.
In your example, the p-value is associated to a z-score of the normal distribution. Your notation here might also be confusing since $H_O$ is commonly used for the null hypothesis.
