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77julia77 [94]
2 years ago
11

A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the un

iversity would like a 0.90 probability that the sample proportion is within 0.112 or less of the population proportion.
a) What is the smallest sample size to meet the required precision? (There is no estimation for the sample proportion.) (Enter an integer number.)
Mathematics
1 answer:
ss7ja [257]2 years ago
3 0

Answer:

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

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

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

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

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 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64

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 0.112 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 have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

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Studentka2010 [4]

Answer:y=4x+6

Step-by-step explanation:

We have the information that the slope is 4 and the line goes through the point (-2,-2). With this information, we can make a linear equation in a point slope form (y - y_{1}= m * (x - x_{1}), so the equation would be y+2=4(x+2), or simplified, y+2=4x+8. in order to solve for y (to make it a slope-intercept equation), we must subtract 2 from both sides. This gives us the equation y=4x+6. Hope this helps!

4 0
3 years ago
You have $60 and your sister has $120. You are saving $14 per week and your sister is saving $10 per week. How long will it be b
tigry1 [53]

Answer:

15 weeks

The amount of money is  270

Step-by-step explanation:

You: 60 +14x

Sister: 120+10x

Set them equal to each other

60+14x = 120+10x

Subtract 10x from each side

60+4x= 120

Subtract 60 from each side

4x= 60

Divide by 4

4x/4 = 60/4

x = 15

15 weeks

The amount of money is 120+10*15 = 120+150 = 270

3 0
3 years ago
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PLEASE HELP im super confused
FinnZ [79.3K]

Answer:

7 Quarters and 3 dimes

Step-by-step explanation:

You have to find how many quarters (0.25) and dimes (0.10) are in $2.05. There are 7 quarters, which will add up to $1.75. You can't have 8 quarters because then you would have 2 dollars, and there wouldn't be enough for a dime, there would only by 5 cents left, or a nickle. Then, you find out how many nickels you need, which is 3.

.10x3=.30. 1.75+0.3=2.05.

I hope you understood:)

4 0
2 years ago
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Studentka2010 [4]

The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

<h3>How to find the numeric value of an expression?</h3>

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

More can be learned about the numeric value of an expression at brainly.com/question/14556096

#SPJ1

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1 year ago
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ehidna [41]
(-5/6)+(-5/6) have the same denominator (number at bottom of fraction), so all you have to do is add the numerator(top number). So -5 +-5 =-10 . Now you have -10/6, which simplifies to -5/3. 
Hope this helps :)
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3 years ago
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