Respuesta :
Answer:
Option A
Step-by-step explanation:
Given information:
[tex]n_1=10, n_2=10[/tex]
[tex]x_1=3, x_2=5[/tex]
Using the given information we get
[tex]p_1=\frac{x_1}{n_1}=\frac{3}{10}=0.3[/tex]
[tex]p_2=\frac{x_2}{n_2}=\frac{5}{10}=0.5[/tex]
The formula for confidence interval for the difference of proportions is
[tex]C.I.=(p_1-p_2)\pm z*\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}[/tex]
From the standard normal table the value of z* at 5% confidence interval is 1.96.
Substitute the given values in the above formula.
[tex]C.I.=(0.3-0.5)\pm z*\sqrt{\frac{0.3(1-0.3)}{10}+\frac{0.5(1-0.5)}{10}}[/tex]
[tex]C.I.=-0.2\pm (1.96)\sqrt{0.021+0.025}[/tex]
[tex]C.I.=-0.2\pm (1.96)\sqrt{0.046}[/tex]
[tex]C.I.=-0.2\pm 0.42[/tex]
[tex]C.I.=(-0.2-0.42,-0.2+0.42)[/tex]
[tex]C.I.=(-0.62,0.22)[/tex]
Therefore, the correct option is A.
