How to check hypothesis by using Pearson's criteria ( $\chi^2$ test), that
$H_0:$ random variable $X$ is normally distributed
given that $k=7$ (count of intervals) and $\alpha=0.1 $ (significance level).
I do understand how you would have to approach problem where you would have to check simple hypothesis, like, for example,
$H_0:$ mean value of pages read by student of computer science faculty per day is greater than or equal 10, given that:
- $n=50$ (test group members)
- $\bar{x}=11.7$
- $s=1$
Then I would define
$H_a$ as: mean value of pages read by student of computer science faculty per day is less than 10.
and calculate $$z=\frac{\bar{x}-\mu_0}{\sigma /\sqrt{n}}$$ and look up P-Value from normal curve areas table. Then comparing P-value against $\alpha$ would determine that $H_a$ would be rejected and therefore $H_0$ would be approved.
But how do I approach my problem?
$$H_0: X\sim N(\mu,\sigma^2)$$ $$H_a: X\nsim N(\mu,\sigma^2)$$