1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mihalych1998 [28]
3 years ago
7

In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha

s been charged with conducting a sample survey to obtain more current information. (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 0.09? Use a 95% confidence level. (Round your answer up to the nearest whole number.)
Mathematics
1 answer:
Afina-wow [57]3 years ago
4 0

Answer:

A sample size of 79 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}.

For this problem, we have that:

\pi = 0.21

The margin of error 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.  

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 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

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

0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}

0.09\sqrt{n} = 1.96\sqrt{0.21*0.79}

\sqrt{n} = \frac{1.96\sqrt{0.21*0.79}}{0.09}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.21*0.79}}{0.09})^{2}

n = 78.68

Rounding up to the nearest whole number.

A sample size of 79 is needed.

You might be interested in
What is the area of this trapezoid?
Misha Larkins [42]

Answer:

132 in

Step-by-step explanation:

rectangle- 12(8)=96

triangle 1- 3(12)= 36 divide by 2 = 18

triangle 2- same as tri. 1

rapeziod- 96+18+18=132

4 0
3 years ago
If 16 key chains cost cost $19.68 how much do 25 key chains cost
Vsevolod [243]
We know how much 16 keychains is, now we need to find how much one is.

19.68 / 16 = $1.23

$1.23 is the price of one keychain, now you can multiply that by 25 to see how much 25 keychains cost.
6 0
3 years ago
Read 2 more answers
How to solve x+3y=3 and 2x-3y=-12
Sever21 [200]
Get x on one side then you can use substitution
So, change x+3y=3 to x= -3y+3
Then plug in x to other equation to find y
2(-3y +3)-3y=-12
-6y + 6 -3y = -12
-9y = -18
Divide both sides by negative nine to find y
y = 2
Then plug in to original equation to find x
x + 3(2) = 3
x + 6 = 3
x = -3
So, y = 2 and x = -3
3 0
3 years ago
Read 2 more answers
If a cell has a volume of 3nm, what are the surface area and the volume of the cell?
harkovskaia [24]
A cell has a radius: r = 3 nmThe surface area of a cell:A = 4 r² π = 4 · 3² π = 4 · 9 π = 36 π nm²The volume of a cell:V = 4/3 r³ π = 4/3 · 3³ π = 4 · 9 π = 36 π nm³Answer: The surface area is 36 π nm² and the volume is 36 π nm³.
7 0
3 years ago
Which of these are a trinomial
Salsk061 [2.6K]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

D) c^2+c+6

»»————- ★ ————-««  

Here’s why:  

  • A trinomial is a expression that consists of three terms.
  • A term can be a number, variable, or both numbers and variables that are multiplied together.
  • Answer choice 'D' has three terms, c², 'c', and '6'. Therefore, it is a trinomial.

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

8 0
3 years ago
Other questions:
  • You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed?
    10·1 answer
  • You spend half of your money on a movie ticket. Then you spend half of what you have left to buy a large popcorn. Then you spend
    10·1 answer
  • Write a proportion and show work
    13·2 answers
  • What is the measure of each exterior angle of a regular triangle
    12·2 answers
  • How many triangles exist with the given angle measures?
    10·1 answer
  • Andrea bought tacos from a food truck and left a 25% tip of $2.00.
    6·1 answer
  • eight wooden spheres with radii 3 in. are packed snugly into a square box 12 in. on one side. the remaining space is filled with
    8·1 answer
  • Alexandra is following a recipe that requires 3/4 a cup of water she needs to make 10 servings how many cups of water does Alexa
    6·1 answer
  • Pls help me ASAP i need help
    5·2 answers
  • Hruuuuuuu? wyddd?? boi? gurl? other? idrk just ask or answer
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!