Answer:
Therefore WE accept the Null hypothesis [tex]H_0[/tex] That 50.0% versus 52.4%.difference is real
Step-by-step explanation:
Sample size A [tex]n_a=100[/tex]
Sample size B [tex]n_b=250[/tex]
Positive draw from box A [tex]n_a=50[/tex]
Positive draw from box b [tex]n_b=131[/tex]
Generally the equation for Probability of Positive draw from Box A is mathematically given by
[tex]P_1=\frac{50}{100}[/tex]
[tex]P_1=50%[/tex]
Therefore
[tex]1-P_1=50\%[/tex]
Generally the equation for Probability of Positive draw from Box A is mathematically given by
[tex]P_1=\frac{131}{250}[/tex]
[tex]P_1=52.4%[/tex]
Therefore
[tex]1-P_1=47.6\%[/tex]
Generally the equation for Standard error S.E is mathematically given by
[tex]S.E=\sqrt{\frac{n_1(p_1)*(1-P_1)}{n_1^2}+\frac{n_2(P_2(1-p^2))}{n_2^2}}[/tex]
[tex]S.E=\sqrt{\frac{100(0.50)*(50)}{100^2}+\frac{(250)(0.524(47))}{250^2}}[/tex]
[tex]S.E=0.592[/tex]
[tex]S.E=59.2\%[/tex]
Therefore
[tex]Z=\frac{50-52.4}{59.2}[/tex]
Generally
[tex]P value P>0.05[/tex]
Therefore WE accept the Null hypothesis [tex]H_0[/tex] That 50.0% versus 52.4%.difference is real
