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lukranit [14]
2 years ago
14

TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streamin

g is gaining in popularity. A poll reported that 56% of 2348 American adults surveyed said they have watched digitally streamed TV programming on some type of device.
a. Calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time.
b. What sample size would be required for the width of a 99% CI to be at most .05 irrespective of the value P?
Mathematics
1 answer:
yarga [219]2 years ago
7 0

Answer:

a)

The 99% confidence interval for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.5336, 0.5864). This means that we are 99% sure that the true proportion of all adult Americans who watched streamed programming up to that point in time is between these two values.

b)

A sample size of 664 is required.

Step-by-step explanation:

Question a:

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}.

A poll reported that 56% of 2348 American adults surveyed said they have watched digitally streamed TV programming on some type of device.

This means that \pi = 0.56, n = 2348

99% confidence level

So \alpha = 0.01, z is the value of Z that has a p-value of 1 - \frac{0.01}{2} = 2.575, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.56 - 2.575\sqrt{\frac{0.56*0.44}{2348}} = 0.5336

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.56 + 2.575\sqrt{\frac{0.56*0.44}{2348}} = 0.5864

The 99% confidence interval for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.5336, 0.5864). This means that we are 99% sure that the true proportion of all adult Americans who watched streamed programming up to that point in time is between these two values.

b. What sample size would be required for the width of a 99% CI to be at most .05 irrespective of the value P?

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

This sample size is given by n, with M = 0.05 and \pi = 0.5.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 2.575\sqrt{\frac{0.5*0.5}{n}}

0.05\sqrt{n} = 2.575*0.5

Dividing both sides by 0.05.

\sqrt{n} = 2.575*10

(\sqrt{n})^2 = (2.575*10)^2

n = 663.1

Rounding up:

A sample size of 664 is required.

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Answer:

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Step-by-step explanation:

Given that:

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marusya05 [52]

Answer:

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

\hat p =\frac{955-812}{955}= 0.150

0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131

0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169

And the 90% confidence interval would be given (0.131;0.169).

Step-by-step explanation:

We have the following info given:

n= 955 represent the sampel size slected

x = 812 number of students who read above the eighth grade level

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

\hat p =\frac{955-812}{955}= 0.150

The confidence interval for the proportion  would be given by this formula

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

For the 90% confidence interval the significance is \alpha=1-0.9=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution and we got.

z_{\alpha/2}=1.64

And replacing into the confidence interval formula we got:

0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131

0.150 + 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.169

And the 90% confidence interval would be given (0.131;0.169).

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3 years ago
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where both f(x),g(x) are continuous functions, then h(x) is also continuous where defined, i.e. where g(x)\neq0

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To solve this equation, we can use the formula x^2-sx+p=0

It means that, if the leading terms is 1, then the x coefficient is the opposite of the sum of the roots, and the constant term is the product of the roots.

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2 years ago
Please show work and solve it! 100 points! n(n-7)=0
Dmitriy789 [7]
Step by step. :)


STEP
1
:
Equation at the end of step 1
0 - 7n • (n - 7) = 0
STEP
2
:
Equation at the end of step 2
-7n • (n - 7) = 0
STEP
3
:
Theory - Roots of a product
 3.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

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Solving a Single Variable Equation:
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 Multiply both sides of the equation by (-1) :  7n = 0


Divide both sides of the equation by 7:
                     n = 0
Solving a Single Variable Equation:
 3.3      Solve  :    n-7 = 0 

 Add  7  to both sides of the equation : 
                      n = 7



This is what i got! if i’m wrong i’m so sorry
but i tried. have a amazing day☺️☺️
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2 years ago
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