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Pavel [41]
3 years ago
9

In early 2012, the Pew Internet and American Life Project asked a random sample of U.S. adults, "Do you ever ... use Twitter or

another service to share updates about yourself or to see updates about others?" According to Pew, the resulting 95% confidence interval is (0.123, 0.177). Does this interval provide convincing evidence that the actual proportion of U.S. adults who would say they use Twitter differs from 0.16? Justify your answer.
Mathematics
1 answer:
8090 [49]3 years ago
3 0

Answer:

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

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Solve the system by substitution.<br> y = -7x. y = -5x + 10​
ohaa [14]

Answer: (-5,35)

Step-by-step explanation:

-7x=-5x+10

Get x on one side by adding 5x

-2x=10

Simplify by dividing by -2

X=-5

Substitute into y=-7x

Y=-7(-5)

Simplify

Y=35

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Parallel lines "a" and "b" are cut by a transversal "c." What is "R" in the diagram below?
belka [17]

Answer:

I'm guessing it's 70°

Step-by-step explanation:

in the image above you can see I circled the 70°

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4 0
2 years ago
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the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle
inna [77]

Answer:

2m

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

A = \frac{1}{2}bh

They give us the area as 6m^2, so let's include it in the equation.

6 = \frac{1}{2}bh

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that h = b-4

So replace h in the equation with b-4.

You will now get:

6 = \frac{1}{2}b(b-4)

Now we can work towards solving. Let's get simplifying.

12 = b(b-4)\\12 = b^2 - 4b\\

bring everything to one side so we can make a quadratic and factor:

0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2

We get that b=6.

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that h = b - 4, so to find h, we just sub in our b value into that.

h = (6) - 4 = 2

We find that h=2

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2 years ago
Another type of subtraction equation is 16-b=7. Explain how you would sole this equation then solve it.
sladkih [1.3K]

Answer: B = 9


Step-by-step explanation:


16-b=7

Rearrange so we can subtract 16 by 7

16 - 7 = 9


Substituting 9 for b and making sure it's correct.

16 - 9 = 7


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3 years ago
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