Can someone please help me with this question

In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent (Pew Research, June 5, 2014). An independe

enot [183]

Answer:

a)

$n = (\frac{z\sqrt{0.16*0.84}}{0.03})^2$ , in which z is related to the confidence level.

b) A sample size of 991 is needed.

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 is:

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

In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent

This means that $\pi = 0.16$

a. What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03 (round up to the next whole number).

This is n for which $M = 0.03$ . So

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

$0.03 = z\sqrt{\frac{0.16*0.84}{n}}$

$0.03\sqrt{n} = z\sqrt{0.16*0.84}$

$\sqrt{n} = \frac{z\sqrt{0.16*0.84}}{0.03}$

$(\sqrt{n})^2 = (\frac{z\sqrt{0.16*0.84}}{0.03})^2$

$n = (\frac{z\sqrt{0.16*0.84}}{0.03})^2$ , in which z is related to the confidence level.

Question b:

99% confidence level,

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

$n = (\frac{z\sqrt{0.16*0.84}}{0.03})^2$

$n = (\frac{2.575\sqrt{0.16*0.84}}{0.03})^2$

$n = 990.2$

Rounding up

A sample size of 991 is needed.

8 0

3 years ago

Please help me with this problem :) <br> show ur work please

Marina CMI [18]

Answer:

$\boxed{w = 14.9} \: or \: you \: can \: say \: \underline{\boxed{w = 15} }$

Step-by-step explanation:

$applying \: the \: pythagorean \: rule : \\ {(hyp)}^{2} = {(adj)}^{2} + {(opp)}^{2} : \\ {w}^{2} = {11}^{2} + {10}^{2} \\ {w}^{2} = 221 \\ w = \sqrt{221} \\ \boxed{w = 14.866068747}$

7 0

3 years ago

Will give brainliest to whoever answers right first

oksian1 [2.3K]

Answer:

0.5x+20=0.25x+30, m=40

Step-by-step explanation:

Blue: y=0.5x+20

Red: y=0.25+30

We’re looking for where the y (cost) is equal, so we can set the two equations to each other:

Isolate x:

0.5x+20=0.25x+30

0.5x+20-20=0.25x+30-20

0.5x=0.25x+10

0.5x-0.25x=0.25x+10-0.25x

0.25x=10

x=40

m= 40

7 0

3 years ago

What is the answer to this

weeeeeb [17]

If all the cheese slices have same mass, say m grams

and mass of 3 cheese slices is 27

so,

m+m+m=27

3m=27

or m=27/3

m=9

thus

mass of one cheese slice is 9 grams

3 0

4 years ago

Read 2 more answers

The center of mass is defined as a point on the straight line between two objects with masses m1 and m2 such that L1 / L2 = M2 /

kondor19780726 [428]

We can represent the problem as shown in the attached drawing

L1=x1

L2=x2

L=x------------distance of the center of mass

we have that

L1/L2=m2/m1------------------> L1*m1=L2*m2------------->m2=L1*m1/L2

moment = Md

the moment about O is defined to be

m1*L1+m2*L2=(m1+m2)*L

L=(m1*L1+m2*L2)/(m1+m2)

m1*L1+m2*L2=2*m1*L1--------remember-------------------->L1*m1=L2*m2

L=(2*m1*L1)/(m1+L1*m1/L2)

L=(2*m1*L1)/(m1*L2+L1*m1)/L2=(2*m1*L1)*L2/(L2*m1+L1*m1)

L=(2*L1*L2)/(L1+L2)

the coordinates of the center of mass are (L,0)

4 0

3 years ago

Can someone please help me with this question​

Can someone please help me with this question