Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions \( p_{1} \) and \( p_{2} \) at the level of significance \( \boldsymbol{\alpha} \).
Assume that the samples are random and independent.
Claim: \( p_{1} \neq p_{2}, \alpha=0.01 \)
Sample Statistics: \( \mathrm{x}_{1}=40, \mathrm{n}_{1}=68, \mathrm{x}_{2}=41, \mathrm{n}_{2}=78 \)
Determine whether a normal sampling distribution can be used.
The samples are random and independent. A normal sampling distribution \( \square \) be used because \( n_{1} \bar{p}= \) \( \square \) \( \mathrm{n}_{1} \overline{\mathrm{q}}=\square, \mathrm{n}_{2} \overline{\mathrm{p}}=\square \), and \( \mathrm{n}_{2} \overline{\mathrm{q}}=\square \).
(Round to two decimal places as needed.)
