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kaheart [24]
3 years ago
5

For a 95% confidence interval what would the sample size need to be as it's most conservative to have a 2% margin of error

Mathematics
1 answer:
aleksley [76]3 years ago
8 0

Answer:

<em>The size of the sample 'n' = 2401</em>

Step-by-step explanation:

<u><em>Step:1</em></u>

Given that the margin of error = 2 % = 0.02

The margin of error is determined by

              M.E = \frac{Z_{0.05} \sqrt{p(1-p)} }{\sqrt{n} }

we know that the proportion

               \sqrt{p(1-p)} < \frac{1}{2}

<u><em>Step:2</em></u>

<em>The margin of error is determined by </em>

<em>               </em>0.02 = \frac{1.96( \frac{1}{2} ) }{\sqrt{n} }<em></em>

              \sqrt{n} =  \frac{1.96}{2 X 0.02}

              √n  = 49

Squaring on both sides, we get

                n = 49 × 49

                n = 2401

<u>Final answer:-</u>

<em>The size of the sample 'n' = 2401 </em>

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lawyer [7]

Starting from the Pythagorean identity, we deduce

\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}

If we plug in the value 7/10 for sin(x), we have

\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}

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4 years ago
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klio [65]

2 sqrt(3) -2sqrt(3)

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5 0
4 years ago
If a + b = -6 and x + y + z = -2, what is 8a - 7x - 7z - 7y + 8b
Oxana [17]

Answer:

-34

Step-by-step explanation:

a + b = -6

x + y + z = -2

We want 8a so multiply the first equation by 8

8( a + b) = -6*8

8a+8b = -48

We also want -7x so multiply the second equation by -7

-7(x + y + z) = -2*-7

-7x-7y-7z = 14

Add the two equations together

8a+8b = -48

-7x-7y-7z = 14

-------------------------

8a+8b-7x-7y-7z = -34

Rearranging the order

8a - 7x - 7z - 7y + 8b = -34

5 0
3 years ago
A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would b
nata0808 [166]

Answer:

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.

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:

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

For this problem, we have that:

p = 0.1

95% confidence level

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

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

We need a sample size of at least n, in which n is found M = 0.04.

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

0.04 = 1.96\sqrt{\frac{0.1*0.9}{n}}

0.04\sqrt{n} = 0.588

\sqrt{n} = \frac{0.588}{0.04}

\sqrt{n} = 14.7

(\sqrt{n})^{2} = (14.7)^{2}

n = 216

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.

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4 years ago
A contact center provides incentives based on the number of sales achieved by its
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Answer:

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