Refer to the data set of 20 randomly selected presidents given below. Treat the data as a sample and find the proportion of presidents who were taller than their opponents. Use that result to construct a 95% confidence interval estimate of the population percentage. Based on the result, does it appear that greater height is an advantage for presidential candidates? Why or why not?
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Complete Question
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Answer:
The 95% confidence interval estimate of the population percentage is
[tex] 33.2\% < p < 76.8 \% [/tex]
Step-by-step explanation:
On the data the first value is the height of the president while the other value is the height of his opponent
The sample size is n = 20
Looking at the data we see that out of the 20 presidents that only 11 is taller than their opponent
So the proportion of presidents that are taller than their opponents is
[tex]\^ p = \frac{11}{20}[/tex]
=> [tex]\^ p = 0.55[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p) }{n}} [/tex]
[tex]E = 1.96 * \sqrt{\frac{0.55 (1- 0.55) }{20}} [/tex]
[tex]E = 0.218[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.55-0.218 < p < 0.55+ 0.218 [/tex]
=> [tex]0.332 < p < 0.768 [/tex]
Converting to percentage
[tex](0.332*100)\% < p < (0.768 *100) \% [/tex]
=> [tex] 33.2\% < p < 76.8 \% [/tex]
Related Questions
what is the number 0.0000 04 in standard form
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Answer:
4x10-6 power
you just need to count the spaced or numbers till you get to 4 then put 10 then to the power of whatever and its -6 because it started from a small number
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Answer:
C
Step-by-step explanation:
Y= -2(3)^2 - 3(3) -6
Y= -2(9) -9 - 6
Y= -18 - 15
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The cafeteria has 28 bottles of orange juice and 14 bottles of apple juice. An equal number of orange and apple juice are displayed in each row. What is the greatest number of orange juice bottles can be in each row?
Shayla says each row will have 28 orange juice bottles but Marcos says there will be 14 bottles in each row. Who is correct: Shayla or Marcos?
Answers
Answer:
The greatest number of orange juice bottles that can be displayed with the apple juice is 14. But if you want it in rows, its 2 or 8.
Step-by-step explanation:
Answer:
Marcus is right: 14 orange juicefind the y-intercept and slope of the function’s graph, and find the equation for the function using the table in the picture.
y- intercept:
slope:
equation:
Answers
m = (y2-y1)/(x2-x1)
m = (9-5)/(3-2)
m = 4
Substitute the values in y= mx + c,
5 = (4)(2) + c
5 = 8 + c
c = -3
Thus, the equation is y= 4x -3
The y intercept is -3 and the slope of line is 4 .
Then the equation of line will be : y= 4x -3
Given,
Points on x and y axis .
Standard equation of line :
y = mx + c
m = slope of line
c = y intercept
Now
Firstly find out the slope of line ,
m = (y2-y1)/(x2-x1)\
m = (9-5)/(3-2)
m = 4
Now to calculate the value of y intercept
Substitute the values in y= mx + c,
5 = (4)(2) + c
5 = 8 + c
c = -3
Thus, the equation is m = (y2-y1)/(x2-x1)
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Answers
Answer:
25r +30j = 460
r - j = 3
Step-by-step explanation:
Let r and j represent Riley's hours and Jace's hours, respectively. The equations could be ...
25r +30j = 460
r - j = 3
__
The solution is (r, j) = (10, 7).
Given that 2x + 1 =5, what is the value of (x+3)^3
Answers
Answer: 125
Step-by-step explanation:
First, solve for x in the first equation.
1) Subtract 1 from both sides.
2x = 4
2) Divide by 2 on both sides.
x = 2
Next, substitute the value of x into the second expression.
(2 + 3)^3
= 5^3
= 125
Answer:
The value of (x + 3)³ is 125.
Step-by-step explanation:
First, we have to find the value of x.
To do so, start with the first equation, 2x + 1 = 5.
We can easily solve this equation to find the value of x.
First, start by subtracting 1 from each side.
This leaves us with 2x = 4.
Next, divide by two on each side.
This will leave us with the answer x = 2.
Now we know the value of x = 2.
All that's left to do is substitute the value of x, 2, for x.
First, start with the second equation (x + 3)³.
We know that x is equal to 2, so we can enter 2 for x.
We then have the equation (2 + 3)³.
Next, solve.
Add the 2 and the 3 together.
Now, the equation is 5³.
5³ is equal to 5 · 5 · 5
5 · 5 · 5 = 125
To sum up,
We found out that x = 2
Using 2 for x, we found out that (x + 3)³ is equal to 125.
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18. Identify the conclusion:
Answers
Answer:
Hypothesis: It is January
Conclusion: There is snow
Step-by-step explanation:
COnditionals are in the form If p, then q.
P is the hypothesis.
Q is the conditional.
If (It is January), then (there is snow).
If and then are not included in the hypothesis and conclusion, respectively.
Hypothesis: It is January
Conclusion: There is snow
What is Hypothesis and Conclusion ?
The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis. Hypotheses followed by a conclusion is called an If-then statement or a conditional statement. This is noted as. p→q. This is read - if p then q. A conditional statement is false if hypothesis is true and the conclusion is false.
Conditionals are in the form if P, then Q.
P is the hypothesis.
Q is the conclusion.
If It is January, then there is snow.
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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x=
Answers
Answer:
x = -28
Step-by-step explanation:
x-(-5) = x + 5
x + 5 = -23
-23 - 5 = -28
x = -28
x-(-5)-23
X+5=-23
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
x²+4x-525
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x²+4x-525
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Answer:
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
[tex]if \: the \: numbers \: of \: shirts \: is \: s.\\ if \: the \: numbers \: of pants \: is \: p. \\then \: the \: inequality \: that \: represents \: \\ the \: numbers \: of \: shirts \: and \: pants \: you \: can \: afford \: is : \\ 9.5s \: + \: 16p \: = 24.[/tex]
Answer:
9.5s + 16p = 24
Step-by-step explanation:
k12
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Answers
Answer:
4.5
Step-by-step explanation:
250 mL= 0.25 L 500 mL= 0.5 L 750mL= 0.75 L+3L
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
If x=1, then f(x)= undefined
Step-by-step explanation:
1*1=1
1-1=0
0/0
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((1*1)-1)/(1-1)
(1-1)/(1-1)
0/0
0/0=Undefined
f(x)= undefined