What must tony deposit today so he will have $60,000 in four years

g A researcher wants to construct a 95% confidence interval for the proportion of children aged 8-10 living in Atlanta who own a

Helga [31]

Answer:

The sample size needed is 2401.

Step-by-step explanation:

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 of the interval is:

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

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 $Z = 1.96$ .

Estimate the sample size needed if no estimate of p is available so that the confidence interval will have a margin of error of 0.02.

We have to find n, for which M = 0.02.

There is no estimate of p available, so we use $\pi = 0.5$

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}$

$n = 2401$

The sample size needed is 2401.

7 0

2 years ago

Read 2 more answers

How many solutions exist for the given equation? 0.75(x 40) = 0.35(x 20) 0.35(x 20) zero one two infinitely many

zimovet [89]

Answer:

One solution

Step-by-step explanation:

0.75 (x + 40) = 0.35 (x + 20) + 0.35 (x + 20)

0.75x + 30 = 0.35x + 7 + 0.35x + 7

0.75x + 30 = 0.7x + 14

0.05x + 30 = 14

0.05x = -16

x = -320

Hope this helps!

7 0

1 year ago

one-third of the people from country A claim that they are from country B, and the rest admit they are from country A. One-fourt

In-s [12.5K]

Answer: 3 : 2

Step-by-step explanation:

Let A represents the total population of country A and B represents the total population of country B.

According to the question,

$\text{The population of country A that admit they are from B} = \frac{1}{3}\text{ of }A$

⇒ $\text{ The population of A that admit they are from country A }= A - \frac{1}{3} \text{ of } A$

$= \frac{3-1}{3} A$

$= \frac{2}{3} A$

$\text{The population of country B that admit they are from A} = \frac{1}{4}\text{ of }B$

⇒ $\text{ The total population that claims that they are from A }= \frac{2}{3} A +\frac{1}{4} B$

But, Again according to the question,

The total population that claims that they are from A = one half of the total population of A and B.

⇒ $\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}(A+B)$

⇒ $\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B$

⇒ $\frac{2}{3} A - \frac{1}{2}A= \frac{1}{2}B-\frac{1}{4} B$

⇒ $\frac{4}{6} A - \frac{3}{6}A= \frac{2}{4}B-\frac{1}{4} B$

⇒ $\frac{1}{6} A = \frac{1}{4} B$

⇒ $A =\frac{6}{4}B$

⇒ $\frac{A}{B} =\frac{3}{2}$

8 0

3 years ago

you go to a restaurant and spent 36.43 on food. if you give the waitress an 18% tip how much money would you get the waitress bi

kenny6666 [7]

Answer:

$43.03

Step-by-step explanation:

18% of $36.43 = $6.60 (6.5574)

$6.60 + $36.43 (price of food without tip)

$6.60 + $36.43 = $43.03

7 0

3 years ago

The vertex angle of an isosceles triangle measures 64 degrees. What is the measure of its base angles?

Dvinal [7]

So hmmm check the picture below

in an isosceles triangle, two sides are equal, and thus the angles those twin legs make, are also twin angles

let's say the angle made is "a", so all internal angles will be 64 + a + a = 180
or 64 + 2a = 180

thus 2a = 180 - 64 => 2a = 116, thus a = 116/2

7 0

3 years ago