Check if the requirements for applying a normal distribution to compare two population proportions are met. If they are, conduct a test of the claim using the specified significance level. Assume the samples are randomly chosen and independent.
Claim: $p_1\ne p_2$, $\alpha =0.01$
Sample statistics:
Group $1$: $48$ successes out of $90$ trials
Group $2$: $52$ successes out of $100$ trials