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?
Answers
Complete Question
The data for this question is shown on the first uploaded image
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]
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Answer:
(x+25)(x-21)
Step-by-step explanation:
x²+4x-525
=x²-21x+25x-525
=x(x-21)+25(x-21)
=(x+25)(x-21)
Answer:
(x+25)(x-21)
Step-by-step explanation:
x²+4x-525
multiply to get -525
add to get 4
x²+4x-525
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2.25x=27
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Use the conditional statement "If it is January, then there is snow." for questions 17 - 18.
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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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Answers
Answer:
x = -28
Step-by-step explanation:
x-(-5) = x + 5
x + 5 = -23
-23 - 5 = -28
x = -28
x-(-5)-23
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Answer:
25x37=925
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
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Step-by-step explanation:
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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
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0/0
You can't divide by 0, so anything that is divided by 0 is undefined.
((1*1)-1)/(1-1)
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You have at most $24 to spend at a store. Shirts cost $9.50 each, and pants cost $16 each. Let s be numbers of shirts and p be numbers of pants. Write an inequality that represents the numbers of shirts and pants you can afford.
Answers
Answer:
[tex]9.5s \: + \: 16p \: = 24.[/tex]
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:
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Step-by-step explanation:
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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
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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
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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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Step-by-step explanation:
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Answers
Answer:
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Answers
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Answer:
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