Respuesta :
Answer:
there is no enough evidence to say that the approval rating of President Obama has changed.
Step-by-step explanation:
We have to construct a confidence interval for the variation in the approval proportion of President Obama.
The sample of 2009 show an approval of p=0.53.
The sample of 2010 show an approval of p=0.50.
The difference between proportions is:
[tex]\Delta p=p_2-p_1=0.50 -0.53=-0.03[/tex]
The estimated standard deviation is:
[tex]s=\sqrt{ \frac{p_2*(1-p_2)}{n_2} +\frac{p_1*(1-p_1)}{n_1}}\\\\s=\sqrt{ \frac{0.50*0.50}{1024} +\frac{0.53*0.47}{1010}}=\sqrt{0.000491}=0.0222[/tex]
To construct a 90% confidence interval, the z-value is z=1.645.
Then, the 90% can be constructed as:
[tex]\Delta p-z\sigma\leq\pi_2-\pi_1\leq \Delta p+z\sigma\\\\-0.03-1.645*0.0222 \leq\pi_2-\pi_1\leq -0.03-1.645*0.0222\\\\-0.03-0.04\leq\pi_2-\pi_1\leq -0.03+0.04\\\\-0.07\leq\pi_2-\pi_1\leq 0.01[/tex]
As the confidence interval upper limit is still over zero, this shows that there are chances that the approval rating has not changed in favor of President Obama.
Then, there is no enough evidence to say that the approval rating of President Obama has changed.
(Note: there would be evidence of change in the approval if the CI does not inclues the value 0 within their limits).
Answer:
Adults polled on April 27, 200927,200927, comma, 2009 were more likely to approve of President Obama's performance than adults polled on September 3, 20143,20143, comma, 2014
Step-by-step explanation:
