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loris [4]
3 years ago
7

You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Co

ke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number
Mathematics
1 answer:
Alex Ar [27]3 years ago
3 0

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

ME=0.03 the margin of error desired

Conf= 0.95 the level of confidence given

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)  

the critical value for 95% of confidence is z=1.96

We can use as estimator for the population of interest \hat p=0.5. And on this case we have that ME =\pm 0.03 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)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

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Solve:<br> 3/4 (5 f - 3) = 3/8<br> F=?
VMariaS [17]

Answer:

f= 0.7

Step-by-step explanation:

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3 0
3 years ago
|3x-7|-7=x solve the equation for all values of x
romanna [79]

The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

<h3>What are the solutions to the given equation?</h3>

Given the equation in question;

|3x-7| - 7 = x

First, add 7 to both sides.

|3x-7| - 7 + 7 = x + 7

|3x-7|  = x + 7

Next, remove the absolute value term, this creates a ± on the right side of the question.

|3x-7|  = x + 7

3x-7  = ±( x + 7 )

The complete solution is the result of both the negative and positive portions of the solution.

For the first solution, use the positive of ±.

3x-7  = ( x + 7 )

3x - 7  =  x + 7  

3x - x = 7 + 7

2x = 14

x - 14/2

x = 7

For the second solution, use the negative of ±.

3x-7  = -( x + 7 )

3x-7  = -x - 7

3x + x = -7 + 7

4x = 0

x = 0/4

x = 0

Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

Learn to solve more equation involving absolute value term here: brainly.com/question/28635030

#SPJ1

4 0
1 year ago
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