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:
Hypothesis: It is January
Conclusion: There is snow
Step-by-step explanation:
COnditionals are in the form If p, then q.
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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.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Answers
Answer: 125
Step-by-step explanation:
First, solve for x in the first equation.
1) Subtract 1 from both sides.
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2) Divide by 2 on both sides.
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Answer:
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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.
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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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Answer:
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Answer:
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Answers
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Step-by-step explanation:
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