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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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Step-by-step explanation:

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3 years ago
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Is x = -12 a solution of x^2 +10x+25=49?
Tresset [83]

Answer:

Yes

Step-by-step explanation:

{x}^{2}  + 10x + 25 = 49 \\  {x}^{2}  + 10x + 25 - 49 = 0 \\  {x}^{2}  + 10x - 24 = 0 \\ (x + 12)(x -2 ) = 0 \\  \\ x  + 12 = 0 \\ x =  - 12 \\  \\  \\ x  - 2 = 0 \\x = 2

I hope I helped you^_^

8 0
2 years ago
Which expression is equivalent to 6(4(6x-4y)-5) ?
iren2701 [21]

Answer:

144x - 96y - 30

Step-by-step explanation:

<u>Step 1:  Distribute </u>

6(4(6x - 4y) - 5)

6((4 * 6x) + (4 * -4y) - 5)

6(24x - 16y - 5)

<u>Step 2:  Distribute again </u>

<u />(6 * 24x) + (6 * -16y) + (6 * -5)

144x - 96y - 30

Answer:  144x - 96y - 30

8 0
2 years ago
fresh+cranberries+have+99%+of+water.+partially+dried+cranberries+have+98%+of+water.+jack+picked+100+pounds+of+cranberries.+how+m
Mnenie [13.5K]

Answer:

  50 lb

Step-by-step explanation:

Before drying, the cranberries have ...

  (100% -99%)(100 lb) = 1 lb

of "meat."

After drying, that represents (100% -98%) = 2% of the total weight. Then the total weight is ...

  1 lb = 2%·x

  x = (1 lb)/0.02 = 50 lb

The dried cranberries will weigh 50 lb.

8 0
2 years ago
A textbook store sold a combined total of 477 sociology and math textbooks in a week. The number of sociology textbois sold was
denpristay [2]

Answer:

The correct answer is 218 math textbooks and 259 sociology textbooks.

Step-by-step explanation:

To solve this problem, we can make a system of equations. Let the number of sociology textbooks sold be represented by the variable "s" and the number of math textbooks sold be represented by the variable "m". Using these variables, we can make two equations:

s + m = 477

m + 41 = s

There are many ways to solve this system of equations. One approach we can take is substituting the value for s given by the second equation into the first equation. This is modeled below.

s + m = 477

(m + 41) + m = 477

Combining like terms on the left side of the equation yields:

2m + 41 = 477

Subtracting 41 from both sides of the equation gives us:

2m = 436

Finally, dividing both sides of the equation by 2 gives us:

m = 218

To solve for the number of sociology textbooks, we can substitute into either of our original equations.

m + 41 = s

(218) + 41 = s

s = 259

Therefore, your answer is m = 218 and s = 259, or 218 math textbooks and 259 sociology textbooks were sold.

Hope this helps!

6 0
2 years ago
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