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
antiseptic1488 [7]
3 years ago
11

3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

rtion of all registered voters who would vote for the
Republican governor.
Mathematics
1 answer:
salantis [7]3 years ago
6 0

Answer:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

Step-by-step explanation:

Previous concepts

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

We assume for this case a confidence level of 95%. 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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

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 if we replace the values obtained we got this:

ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346  

You might be interested in
What is the approximate area of a regular pentagon with a side length of 6 feet and a distance from the center to a vertex of 6
Sergio [31]
The answer is 7,776.
6 0
3 years ago
Read 2 more answers
Help please !! Solve -1.6r+5= -7.8
Nikolay [14]

subtract 5 from both sides. -1.6r=-5 divide both sides by-1.6. r=-5/-1.6 simp;ify-5/1.6 to 3.125. r =3.125

5 0
3 years ago
Read 2 more answers
Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles.
ryzh [129]
Well, an interior angle plus an exterior angle has to equal 180°. Also, the sum of the interior angles is represented by this formula: [-2 + n]180, whereas the sum of the exterior angles all add up to 360°, and is represented by this formula: 360/n [let "n" represent the number of sides in every polygon].
4 0
3 years ago
If the sales tax in your city is 11.4%, and an item costs $160 before tax, how much tax would you pay on that item? Round to the
Oksana_A [137]
First we calculate the tax on the item:
11.4%($160) = 11.4(160)/100 = 18.24
hence the tax for the item is $18.24
The total price for the item would be:
160 + 18.24 = 178.24
hence the total price for the item including tax is:
$<span>178.24</span>

7 0
3 years ago
Use the graph below to answer the question that follows:
seraphim [82]
Let's start with our parent function:

f(x) = sin x

One cycle on this graph occurs between 0 and 2π. Therefore, our b-value is one.

There is no vertical shift up. The sinusoidal axis is along y = 0.

The wave is not inverted, it starts at the origin and rises on both the y and x axis. Thus there is no negative value before the function.

The amplitude of the wave is 3. A normal sine wave rises to a maximum of 1, but this is multiplied by 3.

f(x) = 3 sin x

There are an infinite amount of equations that could be used to represent this graph, but this is perhaps the most intuitive.
6 0
3 years ago
Other questions:
  • What is 2/3x=10 one step equations
    9·2 answers
  • PLEASE HELP!!!!! Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which
    7·2 answers
  • A caterer prepared a large ham that weighed 15 1/8 pounds . After cooking , the chef trimmed the ham and removed the bone , so t
    14·2 answers
  • The volume of a sphere is 3,000 m^3. What is the surface area of the sphere to the nearest square meter?
    14·1 answer
  • PLEASE HELPPPPP I NEED TO PASS SUMMER SCHOOL
    11·1 answer
  • Enter an equation in the form of y = MX + b that represents the function described by the graph ​
    7·1 answer
  • Jenna uses 7.9 pints of blue paint and white paint to paint her bedroom walls.
    6·1 answer
  • An analogue clock is gaining three minutes every hour.If you set it to the correct time at 6 p.m. in Saturday,when will it show
    7·1 answer
  • What is the midline equation of y = -4sin (2x - 7) + 3?
    15·2 answers
  • In the equation 2x = 36 - 8, what is the next step in the equation solving sequence?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!