Presidential approval Many news organizations conduct polls asking adults in the United States if they approve of the job the president is doing. How did President Obama’s approval rating change from August 2009 to September 2010? According to a CNN poll of 1024 randomly selected U. S. adults on September 1-2, 2010, 50% approved of Obama’s job performance. A CNN poll of 1010 randomly selected U. S. adults on August 28-30, 2009 showed that 53% approved of Obama’s job performance. Use the results of these polls to construct and interpret a 90% confidence interval for the change in Obama’s approval rating among all US adults. Based on your interval, is there convincing evidence that Obama’s job approval rating has changed?

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:

The estimated standard deviation is:

To construct a 90% confidence interval, the z-value is z=1.645.

Then, the 90% can be constructed as:

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).

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752