A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

A food company distributes its tomato soup in two cans of different sizes. For the larger can, the diameter has been increased b

Murrr4er [49]

Answer:

Step-by-step explanation:

buenas tardes .....

solucion

Volumen de un cilindro: es igual al área de la tapa por la altura del mismo

A = πD² * h / 4

Lata grande y lata pequeña

Para la lata grande, el diámetro y la altura han aumentado un 20%.

Lata pequeña:

d = 4 cm

h = 3 cm

A 1 = π * (4) ² * 3/4

A1 = 37,70 cm²

Lata grande:

d = 4 * 1,2 = 4,8 cm

h = 3 * 1,2 = 3,6 cm

A2 = π (4,8) ²3,6 / 4

A2 = 65,14 cm²

Si 37,7 representa el 100%

65,14 representación x

x = 170%

El incremento del volumen es de un 70%

6 0

3 years ago

Hello, i'm having trouble with this question in the picture if you know please help me (with workout).

disa [49]

The area of the trapezoid is 4.5cm

4 0

3 years ago