I need help I'm confused

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

Studentka2010 [4]

Using the z-distribution, it is found that the needed sample sizes are:

a) 242

b) 1842

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , 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 $\frac{1+\alpha}{2}$ .

The margin of error is:

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

99% confidence level, hence $\alpha = 0.99$ , z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$ , so $z = 2.575$ .

Item a:

The estimate is:

$\pi = 0.223 - 0.189 = 0.034$

The sample size is <u>n for which M = 0.03</u>, then:

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

$0.03 = 2.575\sqrt{\frac{0.034(0.966)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.034(0.966)}$

$\sqrt{n} = \frac{2.575\sqrt{0.034(0.966)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.034(0.966)}}{0.03}\right)^2$

$n = 241.97$

Rounding up, a sample of 242 is needed.

Item b:

No prior estimates, hence $\pi = 0.5$ is used.

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

$0.03 = 2.575\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{2.575\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.5(0.5)}}{0.03}\right)^2$

$n = 1841.8$

Rounding up, a sample of 1842 is needed.

For more on the z-distribution, you can check brainly.com/question/25404151

5 0

3 years ago

Which value of x is in the domain of f(x) = square root of x-5

Gelneren [198K]

The answer is A. x= 5

3 0

3 years ago

Let f(x)=16^x, find f(1/4)

sergejj [24]

Answer:

2

Step-by-step explanation:

$f( \frac{1}{4} ) = {16}^{ \frac{1}{4} } = \sqrt[4 ]{16} = 2$

That's it, hope you enjoyed it.

6 0

3 years ago

Simplify: 3x – 5 + 23x – 9

padilas [110]

Simple form of equation 3x – 5 + 23x – 9 =<u> 26x-14</u>

<h3>Further Explanation </h3>

Linear Equation in One Variable is an equation that has a variable and the exponent number is one.

Can be stated in the form:

$\large {\boxed {\bold {ax = b}}$

or

ax + b = c, where a, b, and c are constants, x is a variable

Whereas Linear Equation in two Variable is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

$\large {\boxed {\bold {ax + bx = c}}}$

x, y = variable

There are several ways to solve an equation

• Add / Subtract / divide / multiply the same value on both sides

• Combine like terms

• Factoring

• Expanding

Like terms are terms whose variables and their exponents are the same.

You can combine and add terms

The algebraic form of 3x - 5 + 23x - 9 is a Linear Equation in One Variable, can be simplified:

• 1. Combine like terms

(3x + 23x) + (-5 - 9)

• 2. Add like terms:

26x -14

<h3>Learn more </h3>

an algebraic expression

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4 0

3 years ago

Read 2 more answers

What is the absolute value of -10? How do you know this? please heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp please

Delvig [45]

Answer:

The absolute value of -10 is -10

Step-by-step explanation:

Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative.

...

Absolute Value (For example)

|6| = 6 means the absolute value of 6 is 6.

7 0

3 years ago

Read 2 more answers