I'm studing $\chi^2$ test. I generated sample size 50 elements of uniform distribution ($U(x, \frac{-3}{2}, \frac{3}{2})$). After that, I assume that it has the form $N(x, 0, 1)$ and take it as the null hypothesis $H_0$. I checked the null hypothesis using the chi-squared test $\chi^2$ and $\alpha = 0.05$ as a significance point.
The result confused me a little bit. The thing is that the hypothesis $H_0$ is in line with the sample. Obviously, it’s the wrong result.
How that result can be explained? Is it due to the choice of distribution parameters or what?