A random sample of 500 registered voters from one state was obtained. The party affiliation and sex of each voter was recorded and is listed in the following table. (Follow standard statistical rounding rules for all computations.)
a) A journalist who writes for a statewide newspaper wants to construct a confidence interval for the true proportion of registered voters that are affiliated with Party X. Verify that all requirements for constructing such a confidence interval are met.
b) Construct a 99% confidence interval for the true proportion of registered voters that are affiliated with Party X. Show all work. (Hint: the critical value, the margin of error, p, q, the computation, etc.)
c) The Governor of the state believes that a majority of all registered voters in the state are affiliated with Party X because the confidence interval includes values greater than 50% Does the data in the table support the Governor’s belief? Justify your answer.
Answers
Using the z-distribution, it is found that:
a) There are more than 10 successes and 10 failures in the sample, hence the conditions are met.
b) The 99% confidence interval for the true proportion of registered voters that are affiliated with Party X is (0.43, 0.546).
c) Since the lower bound of the interval is below 50%, the data in the table does not support the Governor's belief.
Item a:
The requirement is that there are at least 10 successes and 10 failures in the sample.
244 out of 500 voters are affiliated with party X, hence 500 - 244 = 256 are not, meaning that there are more than 10 successes and 10 failures in the sample, hence the conditions are met.
Item b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
244 out of 500 voters are affiliated with party X, hence:
[tex]n = 500, \pi = \frac{244}{500} = 0.488[/tex]
99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so [tex]z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.488 - 2.575\sqrt{\frac{0.488(0.512)}{500}} = 0.43[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.488 - 2.575\sqrt{\frac{0.488(0.512)}{500}} = 0.546[/tex]
The 99% confidence interval for the true proportion of registered voters that are affiliated with Party X is (0.43, 0.546).
Item c:
Since the lower bound of the interval is below 50%, the data in the table does not support the Governor's belief.
A similar problem is given at https://brainly.com/question/16807970
Related Questions
Which situation can be represented by this inequality 135 ≤ 10r + 15
Answers
[tex]135\leq 10r +15\\\\\implies 120 \leq 10r\\\\\implies 12 \leq r \\\\\implies r \geq 12 \\\\\text{Interval,}~~ [12,\infty)[/tex]
¿Cuál es la pendiente perpendicular a la pendiente m = 3 ?
Answers
Answer:
The slope of a line perpendicular to a vertical line is zero.
Step-by-step explanation:
Donna bought a notebook for $3.50 and then spent half of her money for a textbook. Next she bought sheet music for $4.00 and then spent half of the remaining money on a calculator. She had $8.00 left. How much money did she start with?
Answers
Answer:
$43.50
Step-by-step explanation:
(Work out backward to find the answer)
Remaining money => $8
=> 8 x 2 = 16
=> 16 + 4 = 20
=> 20 x 2 = 40
=> 40 + 3.50 = 43.50
= $ 43.50
Hence, she had $ 43.50 at the beginning.
Determine the intercepts of the line.
Do not round your answers.
y = 4r +7
Answers
Answer:
(-7/4, 0) (0, 7)
Step-by-step explanation:
I'm assuming r is x
0=4r+7
r=-7/4
y=0r+7
y=7
Estimate the quotient for 608 divided by 23
Answers
Answer:
18
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
When estimating we round to the nearest 1.s.f
Thus...
608 rounded to the nearest 1sf
= 600
and....
23 rounded to the nearest 1sf
=20
Therefore- 600÷ 20 = 30
Hope this helped you- have a good day bro cya)
A rectangular field is ten times as long as it is wide. If the perimeter of the field is 1100 feet, what are the dimensions of the field?
Answers
Answer:
Length = 500, Width = 50
Step-by-step explanation:
EQUATION:
2(10x) + 2x = 1100
20x + 2x = 1100
22x = 1100
x=50
I need to answer the bottom question please help me ASAP
Answers
Answer:
60 degrees
Step-by-step explanation:
Because line ED exists, the sum of 100, 20, and x must be 180. So, just solve for x in the equation 100 + 20 + x = 180
20 + x = 80
x = 60
if Vera is 3 times as old as Zoe and 2 times as old as Paul. And the sum of their ages is 33. what is Zoe's age?
Answers
Answer:
Zoe is 6 years old.
Step-by-step explanation:
Vera - V
Zoe - Z
Paul - P
V = 3Z
Z = [tex]\frac{1}{3}V[/tex]
V = 2P
P = [tex]\frac{1}{2}V[/tex]
V + Z + P = 33
[tex]V + \frac{1}{3}V + \frac{1}{2}V = 33[/tex]
[tex]\frac{6}{6} V + \frac{2}{6}V + \frac{3}{6}V = 33[/tex]
[tex]\frac{11}{6}V = 33[/tex]
[tex]V = 33 * \frac{6}{11}[/tex]
[tex]V = 3 * \frac{6}{1}[/tex]
[tex]V = 18[/tex]
V = 3Z
18 = 3Z
Z = 6
There are 22 players in a football team, 9 play defense, 10 play midfield and 11 play back, 5 play defense only, 4 play midfield only and 6 play attack only. Represent the information on a Venn diagram and find number of players who play all the three positions
Answers
Answer: There are 22 players in a football team, 9 play defense, 10 play midfield and 11 play back, 5 play defense only, 4 play midfield only and 6 ...
Step-by-step explanation:Represent the information on Venn diagram. 2.how many players play all the three positions.
Oliver and Eva are reading the same book. At the beginning of the month, Oliver was on page 43 and Eva was on page 21. Oliver will read 3 pages per day and Eva will read 5 pages per day. Let O represent the page of the book that Oliver is on at the end of tt days into the month, and let E represent the page of the book that Eva is on at the end of tt days into the month. Write an equation for each situation, in terms of t, and determine after how many days, t, Oliver and Eva will be on the same page of the book.
O=
E=
Answer: ____ days per page
days
pages
pages per day
when you answer the question plz put it how i seated put with the answer next to them with the answer just put one of them
Answers
The number of days that it will take Oliver and Eva to be on the same page of the book is 11 days.
Oliver's equation = 43 + 3tEva's equation = 21 + 5tBased on the information given, the equation to solve the question will be:
43 + 3t = 21 + 5t
Collect like terms
5t - 3t = 43 - 21
2t = 22
t = 22/2
t = 11
Therefore, it'll take them 11 days.
Read related link on:
https://brainly.com/question/25700149
if someone helps me with dis ill give u brainliest
Answers
Answer:
4 different answers
Step-by-step explanation:
1.
[(24/3) + (5*2^2)] = 28
2.
[(3 + 5) * 2^2 )]/24 = 32/24 = 4/3
3.
[(24/3 + 5)*2^2] = 52
4.
[(3 + 5*2^2)/24] = 23/24
Answer:
Step-by-step explanation:
1 - 2 + 10 o lw. First find a common denominator. 3 * 5 ... Divide the fraction to get a decimal answer. 21 into a an. Jinit. 5 = 1.25. Find a common.
. एक श्रोताकक्ष की लम्बाई तथा चौड़ाई का अनुपात 3 : 2 है. यदि छत का क्षेत्रफल 600 वर्ग मीटर तथा चार दीवारों (d) 2200 वर्ग मा० का क्षेत्रफल 1500 वर्ग मीटर हो, तो इस कक्ष की ऊँचाई कितनी है ?
Answers
Answer:
.
Step-by-step explanation:
Answer: 2 है यदि छत का क्षेत्रफल 600 वर्ग मीटर तथा चार दीवारों का क्षेत्रफल 1500 वर्ग मीटर हो तो
Step-by-step explanation:
what is 4 1/6÷5 please help
Answers
Answer:
It is 5/6
Step-by-step explanation:
For questions like these use caculator soup you can use it for fractions and much more it shows u how to work the problem out also.
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Upload the entire proof below.
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m
STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m∠1 + m∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m∠1 + m∠2 = m∠1 + m∠3 5.
6. 6.
7. l || m 7.
Answers
Line m and line l are parallel as m∠2 = m∠3
Equation
An equation is an expression that shows the relationship between two or more variables and numbers.
Two angles are said to be supplementary if they add up to 180 degrees.
m∠1 + m∠2 = 180° (Given)
m∠1 + m∠3 = 180° (sum of angles on a straight line)
Hence:
m∠1 + m∠2 = m∠1 + m∠3
m∠2 = m∠3
Line m and line l are parallel as m∠2 = m∠3
Find out more on Equation at: https://brainly.com/question/2972832
solve for x in equation !! ?
Answers
Pretty sure the answer is d
What is the value of v?
Answers
Answer:
34 degrees
Step-by-step explanation:
If you know the 2 interior angles of a triangle, you can find the 3rd.
This is useless since this is a right triangle.
In this case:
v + 46 = 90
v = 34 degrees
You are welcome!
Kayden Kohl
8th Grade Student
can someone pls help me with dis ill give brainliest
Answers
Answer:
274900
Step-by-step explanation:
Convert a number to and from scientific notation, e notation, engineering notation, standard form, and real numbers. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation, engineering notation, standard form and word form formats.
To enter a number in scientific notation use a carat ^ to indicate the powers of 10. You can also enter numbers in e notation. Examples: 3.45 x 10^5 or 3.45e5.
Order of magnitude will also be identified for the calculated standard form. The order of magnitude when written in standard form, is the nth power of 10. For example, 3.4 x 10^5 has an order of magnitude of 5 since 10 is raised to the 5th power.
Answer:
Yes it is written in scientific notation.
Step-by-step explanation:
Scientific notation is --> a x 10^b. where a and b are certain values. This value follows that pattern, so yes it is in scientific notation.
16 is 80% of what number?
O A. 20
O B. 12.8
O C. 500
O D. 128
Answers
Answer:
A. 20
Step-by-step explanation:
1. To solve this problem, instead of doing 80/100 times 16, we can do 100/80 times 16 (inverse of percentage, basically).
[tex]\frac{100}{80} *16[/tex] [tex]\frac{5}{4} *16[/tex] [tex]\frac{80}{4}[/tex] [tex]20[/tex]Therefore, the answer is A. 20.
The following table shows Lane and Rory's scores on the first 5 math quizzes this semester. How many points higher is Rory's average than Lane's average?
Answers
Answer:
0
Step-by-step explanation:
Because Rory's higher average and Lane's higher average is 96 in Quiz 3.
96-96=0
Dеtеrmіnе tһе rаnցе օf tһе fսnсtіօn f(х) = 2х + 1 ԝһеn tһе ԁօmаіn іѕ {-3, 9, 15}.
Answers
Answer:
Range: {-5, 19, 31}
Step-by-step explanation:
Given the linear function, f(x) = 2x + 1, and the domain, {-3, 9, 15}.
In order to determine the range of the given linear function, simply substitute each domain value as inputs into the function.
x = -3f(x) = 2x + 1
f(-3) = 2(-3) + 1
f(-3) = -6 + 1
f(-3) = -5
x = 9f(9) = 2x + 1
f(9) = 2(9) + 1
f(9) = 18 + 1
f(9) = 19
x = 15f(15) = 2x + 1
f(15) = 2(15) + 1
f(15) = 30 + 1
f(15) = 31
Therfore, the range of the function is: {-5, 19, 31}.
Triangle DEF is dilated by a scale factor of 2/3 to form triangle D´E´F´. What is the measure of side DE?
Answers
Answer:
DE = 30
Step-by-step explanation:
Let X be the measure of side DE.
You can write this equation to represent the problem:
[tex]x *\frac{2}{3} =20[/tex]
The measure of DE (x) is multiplied by the scale factor of [tex]\frac{2}{3}[/tex] to become 20.
Solve for x:
[tex]x *\frac{2}{3} =20\\\frac{2x}{3} =20\\2x=60\\x=30[/tex]
DE = 30
Ana is playing a quiz game and needs more than 500 points to advance to the next level. She earns 18 points for each correct answer loses 6 points foWhat is an inequality that represents all the possible combinations of c, the number of correct answers, and w, the number of incorrect answers that Ana can get and move to the next level?
Answers
if the words after " 6 points fo" is "r each incorrect answer" then the answer is
18c - 6w > 500
explanation:
if she answers one correct, she'll get 18 points, so if she gets 18 correct, she'll get 18c points, same goes for each she gets incorrect but loses 6 points is +-6w, or simplified, -6w
Drag each statement to show whether it is true, based on
the graph
Answers
Answer:
see attached
Step-by-step explanation:
The independent variable is the one displayed on the horizontal axis: pounds. The dependent variable is the one shown on the vertical axis: cost.
Then the ordered pair shown represents ...
(pound, cost) = (0.65, 2.20)
That is, the cost of 0.65 pounds is $2.20. The cost per pound is found by dividing cost by pounds:
price per pound = $2.20/0.65 lb
__
There is no information shown regarding the weight or cost of a bag of almonds.
The categorization is shown in the attachment.
-2(2v + 11) + 1 =-5(9v – 4)
Answers
Answer:
v=1
Step-by-step explanation:
-2(2v + 11) + 1 =-5(9v – 4)
Distribute the -2 and -5.
-4v-22+1=-45v+20
Calculate the sum.
-4v-21=-45v+20
Move the variable to the left-hand side and change the sign.
-4v-21+45v=20
Move the constant to the right-hand side and change the sign.
-4v+45v=20+21
Collect like terms.
41v=20+21
Add the numbers.
41v=41
Divide both sides by 41
v=1
Hope this helps :)
Answer:
v = -1/49
Step-by-step explanation:
distribute
-4v - 22 + 1 = 5(9v-4)
add the numbers -21 + 1 = -21
distribute the other parenthesis
-4v - 21 = 45v -20
add 21 to both sides to get v by itself
-4v - 21 + 21 = 45v + 20 + 21
-4v = 45v + 1
substract 45 v on both side now
-4v - 45v = 45v + 1 - 45v
simplify
-49v = 1
divide -49 on both side
v = -1 / 49
The average of max's three tests is an 84 what must he get on a fourth test to raise his average to an 87
Answers
Answer:
He must get a 96% on the fourth test to raise his average to an 87
7. Sid has a board that is 8 5/6
feet long. He cuts a piece off of the board that
is 3 1/4 feet long. How long is the remaining piece of board
Answers
Answer:
5 7/12 feet left
Step-by-step explanation:
Step 1: 8 5/6 - 3 1/4
Step 2: = 67/12 (Put into proper fraction)
Step 3: = 5 7/12
Hope that helps :)
Answer:
5 7/12
Step-by-step explanation:
Given that the board is 8 5/6 feet long.
Cuts off 3 1/4 feet.
8 5/6- 3 1/4
Change fractions into improper fractions.
8 5/6=53/6
3 1/4=13/4
-------------------------------------------------------------
53/6x2/2=106/12
13/4x3/3=39/12
106/12-39/12=67/12
=5 7/12
Hope this helps :)
Choose the best answer.
The area of the face of a quarter is about
O A. 63 cm
OB. 63 m2
O C. 63 mm2
O D. 63 dm?
Answers
Answer:
One face of a US quarter has an area of approximately 461.21 square millimeters.
Step-by-step explanation:
calculate each angle measure.
Answers
Answer:
m1=90
m2=68
m3=112
m4=112
m5=68
m6=56
m7=124
m8=124
i need help with this please
Answers
Consider this expression x^2-(3x+y)+16
Answers
Answer:
x^2-3x-y+16?
Step-by-step explanation:
simplest form already, but can be converted into a proper polynomial.
x^2-3x-y+16