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rodikova [14]
2 years ago
14

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n=500, x=

250,95% confidence nothingless thanpless than nothing ​(Round to three decimal places as​ needed.)
Mathematics
1 answer:
Alla [95]2 years ago
8 0

Answer:

0.5 - 1.96 \sqrt{\frac{0.5(1-0.5)}{500}}=0.456  

0.5 + 1.96 \sqrt{\frac{0.5(1-0.5)}{500}}=0.544  

And the 95% confidence interval would be given (0.456;0.544).  

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".  

Solution to the problem

The confidence interval for a proportion is given by this formula  

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

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

The estimated proportion is :

\hat p =\frac{x}{n}=\frac{250}{500}=0.5

And replacing into the confidence interval formula we got:  

0.5 - 1.96 \sqrt{\frac{0.5(1-0.5)}{500}}=0.456  

0.5 + 1.96 \sqrt{\frac{0.5(1-0.5)}{500}}=0.544  

And the 95% confidence interval would be given (0.456;0.544).  

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The length of a sticky note measures 77 millimeters.express this length in meters explain your thinking include an equation with
Eva8 [605]

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Further explanation:

Given:

The length of sticky notes is measured as 77 millimeters.

Calculation:

Since 1 meter contains 1000 mm, it can be written as follows:

\begin{aligned}1000{\text{mm}}&\to{\text{1meter}}\\{\text{1mm}}&\to\frac{{\text{1}}}{{1000}}{\text{meter}}\\{\text{1mm}}&\to{10^{-3}}{\text{meter}}\\x\,{\text{mm}}&\to x \times {10^{-3}}{\text{meter}} \\ \end{aligned}

Now, substitute 77 for x in above expression to obtain the length of sticky notes in meter as follows:

77\,{\text{mm}}\to77\times{10^{-3}}{\text{meter}}

Thus, the length of the sticky notes is \bf77\times{10^{-3}}{\text{meter}}.

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Answer Details :

Grade: Middle School

Subject: Mathematics

Chapter: linear equation

Keywords:

Millimeters, meter, equation, sticky notes, measurements, length, function, substitution, Mexico, site, direct substitution, elimination, graph, middle term factorization, scientific notation.

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Answer:

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By substitution:

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