I have some difficulties with understanding the output of the KS test in R. Suppose I want to test whether my data follows a exponential distribution with rate 1/117.5 with a significance level $\alpha = 0.05$. I have the following hypothesis:
$H_0$: The data follow the exponential distribution
$H_a$: The data do not follow the exponential distribution
I have the following code in R:
x <- rexp(10000, rate = 1/120) ks.test(x, "pexp", rate = 1/117.5)
and get the output:
One-sample Kolmogorov-Smirnov test data: x D = 0.0132, p-value = 0.06224 alternative hypothesis: two-sided
So, since P > $\alpha$, I can not reject the null? and hence assume my date follows a exponential distribution with rate 1/117.5?
I'm a little lost with the meaning of the P value and the significance level $\alpha$.