Respuesta :
Answer:
1) p1=0.83
2) p2=0.81
3) Option B
4) p=0.82
5) s=0.03
6) z=0.67
7) P=0.50
8) Do not reject H0
Step-by-step explanation:
1) The proportion of Republicans who think the full-body scans should be applied in airports is equal to the ratio between the republicans that think it should over the total Republicans in the poll:
[tex]p=X/n=258/311=0.83[/tex]
2) The proportion of Democrats who think the full-body scans should be applied in airports is equal to:
[tex]p=X/n=294/363=0.81[/tex]
3) As we want to know if there is a difference in the proportions calculated, not if one is higher or lower than the other, the correct option is B:
[tex]H_0:p_1-p_2=0\\\\H_a:p_1-p_2\neq0[/tex]
4) The pooled estimate of a proportion is the average of both proportions:
[tex]\bar{p}=\frac{p_1+p_2}{2}= \frac{0.83+0.81}{2}=0.82[/tex]
5) The standard error can be calculated as:
[tex]s=\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1} +\frac{\bar{p}(1-\bar{p})}{n_2}} \\\\s=\sqrt{\frac{0.82*0.18}{311} +\frac{0.82*0.18}{363}} \\\\s=\sqrt{0.00047+0.00041} =\sqrt{0.00088}=0.03[/tex]
6) The z-statistic can be calculated as:
[tex]z=\frac{p_1-p_2}{s}=\frac{0.83-0.81}{0.03}=\frac{0.02}{0.03}=0.67[/tex]
7) The P-value for z=0.67 is P=0.50 (from the standard normal distribution table).
[tex]2P(Z>|z|)=0.50286[/tex]
8) If the significance level is 0.01, the P-value is bigger than the significance level. The effect is not significanct. The null hypothesis is not rejected.
There is not enough evidence to say that both proportions are different.
A. Do not reject H0
