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 $1 - \frac{\alpha}{2}$ .

The margin of error is of:

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

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that $n = 2161, \pi = \frac{1214}{2161} = 0.5618$

95% confidence level

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

Margin of error:

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

$M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}$

$M = 0.0209$

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

4 0

3 years ago

The cost to ride a ferris wheel is $2.00 per person. The ferris a wheel has a capacity of

irakobra [83]

Answer:

When we have a function f(x), the domain of the function is the set of all the inputs that "work" (Not only in a mathematical way, the context is also important) with the function f(x)

In this case, we have a function M(p) = $2*p

This function represents the amount of money collected depending on the number of people who ride on the ferris whell.

Then p can be only a whole number (we can not have 1.5 people, only whole numbers of people).

And we also know that the maximum capacity of the ferris is 64 people.

Then:

p ≤ 64

And we also should add the restriction:

0 ≤ p ≤ 64

(Because p can't be smaller than zero)

Such that p should also be an integer, then, the domain is:

D: p ∈ Z, p ∈ {0, 1, 2, ..., 64}

7 0

2 years ago