Mathematics, 19.07.2021 20:00 wendisp54x2h

Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?

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The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering n = 1000

Step-by-step explanation:

Incomplete question, so i will suppose this is a sample of 1000.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Of the n respondents, 502 replied that America is doing about the right amount.

Supposing n = 1000 , so $\pi = \frac{502}{1000} = 0.502$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so Z = 1.96 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543$

The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering n = 1000

Answer from: Quest

4 + 5 7/9= 9 7/9

step-by-step explanation:

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confi...

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