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dalvyx [7]
3 years ago
12

Suppose that we want to estimate the true proportion of defectives in a very large shipment of adobe bricks, and that we want to

be at least 95% confident that the error is at most 0.04. How large a sample will we need if:
a) We have no idea what the true proportion might be
b) We know that the true proportion is approximately 0.12?
Mathematics
1 answer:
Alinara [238K]3 years ago
8 0

Answer:

a) n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

b)  n=\frac{0.12(1-0.12)}{(\frac{0.04}{1.96})^2}=253.546  

And rounded up we have that n=254

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 proportion is given by the following formula:  

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

Part a

The margin of error for the proportion interval is given by this formula:  

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

And on this case we have that ME =\pm 0.04 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't know prior estimation for the population proportion we can use \hat p=0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

Part b

For this case we use \hat p =0.12 and if we solve for n we got:

n=\frac{0.12(1-0.12)}{(\frac{0.04}{1.96})^2}=253.546  

And rounded up we have that n=254

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Answer:

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Step-by-step explanation:

The elements that make up a musical fugue are:

The exhibition: It begins with one of the voices presenting the subject (name given to the theme on which a fugue is based). A second voice continues with the answer. The other voices continue alternately between subjects and responses. The exhibition concludes once all the voices have presented the subject or the answer.

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In the first place, he must remember that Bach was a self-taught, he was trained alone and specifically by the study of music itself, by the observation and analysis of other people's compositions, very often of poor significance in front of his own and that he copied, however, of his handwriting. The pedagogical activity of Bach and what he taught: "We must make the fugue of the subject", this means that each subject requires his fugue. Bach added another teaching, "voices must not enter without having something to say, or call before they have said everything they have to say," which means that they have voices should not speak for speaking and that they have no obligation to be always present.

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Answer:

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Step-by-step explanation:

Given

\sqrt[3]{27 x^{3} y^{2} z}

Step 1 of 1

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Learn more about radical notation, refer :

brainly.com/question/15678734

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Answer:

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Step-by-step explanation:

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x * 5 = 120

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