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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

For this problem, we have that:

$\pi = 0.4$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary?

We need a sample size of n.

n is found when M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.4*0.6}{n}}$

$0.02\sqrt{n} = 1.96*\sqrt{0.4*0.6}$

$\sqrt{n} = \frac{1.96*\sqrt{0.4*0.6}}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.96*\sqrt{0.4*0.6}}{0.02})^{2}$

$n = 2304.96$

Rounding up

The minimum sample size necessary is 2305.

8 0

3 years ago

Tell whether the ordered pair is a solution to the system of linear equations. 1 point

Nataly_w [17]

Answer:

Tell whether the ordered pair is a solution to the system of linear equations. 1 point

(-2,-1); 2x – 4y= -8

6x + 5y = -7

3 0

3 years ago

WILL MARK WILL MARK BRAINLEST

patriot [66]

Answer:

d=10.0002

Step-by-step explanation:

Given That:

Height=h=28 inches

Volume=V=732.7 cubic inches

Required:

Diameter of the base of the cone=d=?

Solution:

the formula for the volume of a cone is

re-arranging the terms to get the radius (r)

putting values, we get

to find the diameter we know that diameter is double of the radius so

d=2r

d-2(2.0051)

d=10.0002

4 0

3 years ago

32.4% of 191.2 Round to the nearest thousand

Archy [21]

ANSWER: 61.9488
I think this is the right answer. I hope this helps

5 0

3 years ago