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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Answer 1

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]

Refer To The Data Set Of 20 Randomly Selected Presidents Given Below. Treat The Data As A Sample And

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Answer:

Removing the -6 makes the average go from 4.1 to 5.2

Removing the -6 makes the median go from 4 to 5

Step-by-step explanation:

Average:

-6+3+3+3+3+5+6+6+8+10 = 41

41/10 = 4.1 (This is the mean/average)

If we remove -6, then:

3+3+3+3+5+6+6+8+10 = 47

47/9 = 5.2222 (This would be the new average)

So removing the -6 makes the average go from 4.1 to 5.2

Median:

The median of (-6+3+3+3+3+5+6+6+8+10) is between 3 and 5, so the median is 4.

Without -6, the median of (3+3+3+3+5+6+6+8+10) is 5.

So removing the -6 makes the median go from 4 to 5

The table shows ticket prices for the local minor
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Answers

Answer:

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Answers

a) y= -10.

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At the start of the football game, there were 840 fans in the stadium. It began to rain during halftime, so 10% of the fans went home.
During the 3rd quarter of the game, the visiting team scored five touchdowns, so 25% of the remaining fans went home.
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Answers

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Answers

Answer:

x = 96

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Step-by-step explanation:

x and 84 are supplementary angles.

this means that they add together to make 180.

using this, you can make the following equation:

x + 84 = 180

subtract 84 from both sides of the equation

x + 84 - 84 = 180 - 84

x = 180 - 84

x = 96

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vertical angles are equal.

using this, you can make the following equation:

84 = 3z + 9

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Answer:

(2,[tex]\frac{5}{2}[/tex])

Step-by-step explanation:

Midpoint formula: M=([tex]\frac{x_{1} +x_{2} }{2}[/tex],[tex]\frac{y_{1} +y_{2} }{2}[/tex])

M=([tex]\frac{2+2}{2}[/tex],[tex]\frac{1+4}{2}[/tex])

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A birthday cake was cut into equal pieces, and six pieces were eaten. The
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Answer:

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Step-by-step explanation:

Answer:

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A dependent system of equations has infinite simultaneous solutions

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Answer:

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Step-by-step explanation:

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Answers

Answer:

The probability of selecting a small or white marble is 10/13

Step-by-step explanation:

The total number of marbles is 15 + 11 = 26 marbles

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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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Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

x = 11

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

Answer:

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Answer:

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Answer:

22

Step-by-step explanation:

Step 1: fill in the equation

(3-8)^2-3

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Step 3: solve

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Answer:

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Step-by-step explanation:

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Answers

Answer:

√3

Step-by-step explanation:

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Answers

Answer:

w = xc/y

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