b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

Step-by-step explanation:

Question a:

86.6% out of 3149, so:

0.866*3149 = 2727.

272 used at least one prescription medication.

Question b:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 3149, \pi = 0.866$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876$

For the percentage:

0.856*100% = 85.6%

0.876*100% = 87.6%.

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

7 0

3 years ago

Which ordered pair is a solution to the system of equations?

melisa1 [442]

Answer:

(-2, -3)

Step-by-step explanation:

We assume your system of equations is ...

2x - y = -1
2x -4y = 8

You can subtract the second equation from the first to get

... (2x -y) -(2x -4y) = (-1) -(8)

... 3y = -9 . . . . . collect terms

... y = -3 . . . . . . divide by 3 . . . . this is sufficient to identify the correct answer

Substituting into the first equation, we have ...

... 2x -(-3) = -1

... 2x = -4 . . . . . add -3

... x = -2 . . . . . . .divide by 2

Now, we're sure the answer is (x, y) = (-2, -3).

3 0

3 years ago