A Two-Sample $z$ -Test for Two Population Proportions Is to Be Performed Using

Multiple Choice

A two-sample $z$ -test for two population proportions is to be performed using the $P$ -value approach. The null hypothesis is $H _ { 0 } : p _ { 1 } = p _ { 2 }$ and the alternative is $H _ { A } : p _ { 1 } \neq p _ { 2 }$ . Use the given sample data to find the $p$ -value for the hypothesis test. Give an interpretation of the $p$ -value.
$$n _ { 1 } = 50 , x _ { 1 } = 20 , n _ { 2 } = 75 , \text { and } x _ { 2 } = 15$$

A) $P$ -value $= 0.0032$ ; If there is no difference in the proportions, there is about a $0.32 \%$ chance of seeing the observed difference or larger by natural sampling variation.
B) $P$ -value $= 0.0147$ ; If there is no difference in the proportions, there is about a $1.47 \%$ chance of seeing the observed difference or larger by natural sampling variation.
C) $P$ -value $= 0.0292$ ; If there is no difference in the proportions, there is a $2.92 \%$ chance of seeing the exact observed difference by natural sampling variation.
D) $P$ -value $= 0.0032$ ; There is about a $0.32 \%$ chance that the two proportions are equal.
E) $P$ -value $= 0.0147$ ; There is about a $1.47 \%$ chance that the two proportions are equal.