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vaieri [72.5K]
3 years ago
5

A sociologist wishes to estimate the percentage of the United States population living in poverty. What size sample should be ob

tained if she wishes the estimate the population proportion to be within 2 percentage points with 90% confidence, a) If she uses 1999 estimate of 11.8% obtained from the Current Population Survey. b) She does not use any estimate.
Mathematics
1 answer:
andriy [413]3 years ago
4 0

Answer:

a) We need a sample size of at least 705.

b) We need a sample size of at least 1692.

Step-by-step explanation:

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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

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

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

a) If she uses 1999 estimate of 11.8% obtained from the Current Population Survey.

We need a sample of size at least n

n is found when M = 0.02, \pi = 0.118.

So

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

0.02 = 1.645\sqrt{\frac{0.118*0.882}{n}}

0.02\sqrt{n} = 1.645\sqrt{0.118*0.882}

\sqrt{n} = \frac{1.645\sqrt{0.118*0.882}}{0.02}

(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.118*0.882}}{0.02})^{2}

n = 704.08

Rounding up

We need a sample size of at least 705.

b) She does not use any estimate.

Same thing as above, we just use \pi = 0.5 when do not use any estimate.

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

0.02 = 1.645\sqrt{\frac{0.5*0.5}{n}}

0.02\sqrt{n} = 1.645\sqrt{0.5*0.5}

\sqrt{n} = \frac{1.645\sqrt{0.5*0.5}}{0.02}

(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.5*0.5}}{0.02})^{2}

n = 1691.2

Rounding up

We need a sample size of at least 1692.

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Answer:

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Step-by-step explanation:

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16/24 = 2/3

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Answer

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Answer:

The quadratic polynomial with integer coefficients is y = 81\cdot x^{2}-36\cdot x -19.

Step-by-step explanation:

Statement is incorrectly written. Correct form is described below:

<em>Find a quadratic polynomial with integer coefficients which has the following real zeros: </em>x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}<em>. </em>

Let be r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9} and r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9} roots of the quadratic function. By Algebra we know that:

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Complete parts (a) and (b) using the probability distribution below.
katen-ka-za [31]
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We need the value of ∑X² to work out the variance
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Variance = ∑X² - μ²
Variance  = 13.323 - (3.4)² = 1.763 ≈ 2

Standard Deviation = √Variance = √1.8 = 1.3416... ≈ 1.4

The correct answer related to the value of mean and standard deviation is the option D
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A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin
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Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

T_1cos\theta_1-T_2cos\theta_2=0           (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

T_1sin\theta_1+T_2sin\theta_2-W=0               (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2

Then, you sum the equations:

T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2        (3)

Next, you use the following identity:

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and you obtain in the equation (3):

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With this values you can calculate the value of the another angle, by using the equation (1):

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Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

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