Large sample size for t-test I am working on a physics experiment, and I ran 500 runs to calculate a parameter. I want to use the t-test to see if my mean from 500 runs matches the actual value.


*

*u0: mean is actual value  

*u1: mean is not actual value


When I tried with 100 data first, it returned a high p-value which did not reject the null hypothesis. So I was very happy with my results. However, when I tried with 500 data, it provided me low p-value (<0.05). So I have to reject my hypothesis.
I find this very strange because my mean from 100 data and 500 data are very close. I believe the higher sample size changed that insignificant difference to significant difference.
So what sample size is recommended? Any article that I can look for? 
 A: As has been pointed out already, essentially you have formulated a hypothesis that does not test what you wish to actually show.  Your interpretation of the $p$-value also implies this.
If your intended goal is to show with a high degree of confidence that an empirically estimated statistic is "equivalent" to a theoretically derived parameter, then one correct form of a hypothesis test to establish equivalence might be $$H_0 : |\hat \mu - \mu| \ge \Delta \quad {\mathrm{vs.}} \quad  H_a : |\hat \mu - \mu| < \Delta,$$ where $\mu$ is the theoretical mean, $\hat \mu$ is your estimator of $\mu$, and $\Delta > 0$ is some chosen value that represents your belief of how close these two values must be in order to consider them "equivalent."
This test is a composite hypothesis, which needs to be written as the intersection of two one-sided tests: $$\begin{align*} H_{01} : \hat\mu - \mu \ge \Delta \quad &{\mathrm{vs.}} \quad H_{a1} : \hat\mu - \mu < \Delta, \\ H_{02} : \hat\mu - \mu \le -\Delta \quad &{\mathrm{vs.}} \quad H_{a2} : \hat\mu - \mu > -\Delta. \end{align*}$$  Both $H_{01}$ and $H_{02}$ must be rejected in order to accept $H_a$.  How you proceed from here depends on your assumptions regarding the sampling distribution of the estimator $\hat\mu$.  If you assume it is normal with known variance, then you have two one-sided $z$-tests; if you assume it is normal with unknown variance, then you have two one-sided $t$-tests; and so forth.  Then you want to determine the form of the test statistic, and calculate a $p$-value for this test.
If the $p$-value is sufficiently small, then you will reject $H_0$ and say that the measured mean is "equivalent" to the theoretical mean.  If not, the decision is to fail to reject the null and say that the data gathered contains insufficient evidence to suggest the empirical mean equals the theoretical mean.
Again, I remind you that the notion of "equivalence" or "equality" is necessarily defined by your choice of $\Delta$.  You cannot choose $\Delta = 0$ because the critical region for such a test is the empty set, and such a test will have no power--you will always fail to reject the null.
Finally, this hypothesis is not the only one possible.  Depending on your beliefs about the nature of the sampling distribution of your estimator, other hypotheses may be more appropriate.
A: It's not strange at all. Having a larger sample shrinks your standard errors, improving your ability to reject the null when the sample mean is only slightly different from it. This should be your conclusion: that the sample mean is slightly different from the null hypothesis. Maybe you should worry more about the effect size. In any case, the recommended sample size is "as large as it can get."
