1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aliun [14]
3 years ago
15

The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitor

ies, p, who own a computer with a 99% confidence interval. What is the minimum required sample size the IT Department should use to estimate the proportion p with a margin of error no larger than 5 percentage points
Mathematics
1 answer:
nadya68 [22]3 years ago
3 0

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

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 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

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 0.05 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)  

We can use as an estimator for p \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

You might be interested in
Can someone help me find the volume of this?
GalinKa [24]
To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.
5 0
3 years ago
HELP
TiliK225 [7]
I think it’s B I’m not sure about it but I hate wan I gat it wrong.
8 0
2 years ago
RS=4y+4, ST=3y+4, and RT=43 <br> What is the value of y?
Shkiper50 [21]

The value of y is 5

<h3>How to determine the value </h3>

From the given line, it can be concluded that:

The segment RT is divided into RS and ST

But we have the following parameters

The length of the sides are:

  • RS=4y+4
  • ST=3y+4
  • RT=43

Since RT is RS added to ST:

We have;

RT = RS + ST

substitute the values

43 = 4y + 4 + 3y + 4

collect like terms

43 = 4y + 3y + 4 + 4

Add like terms

43 = 7y + 8

43 = 7y + 8

Make '7y' subject of formula

7y = 43 - 8

7y = 35

Make 'y' the subject of formula

y = 35/ 7

y = 5

Thus, the value of y is 5

Learn more about segments here:

brainly.com/question/2437195

#SPJ1

5 0
1 year ago
I need help please 20 or more points please
Norma-Jean [14]

Answer: V, V, (-5, -5.5)

Step-by-step explanation:

7 0
2 years ago
We have x = 7 so now solve for y by replacing x with 7 in this equation 2x + y = 20
Ivahew [28]

Answer:

y=6

Step-by-step explanation:

2(7)=14.

subtract both sides by 14.

y=6

7 0
3 years ago
Read 2 more answers
Other questions:
  • Here's another. Please help. Thank you :)
    15·1 answer
  • Which of the following is the equation of an ellipse centered at (5,1) having a vertical minor axis of length 4 and a major axis
    12·1 answer
  • The digit 4 in 49,308 has a value as much as the 4 in 4,061
    11·2 answers
  • Can somebody help me with this?
    5·1 answer
  • Velvet fabric costs $11.49 a yard. Yvette buys 9.3 yards. Yvette's estimated cost of the velvet is
    13·1 answer
  • Bob has $150 in his savings account and saves $40 per month.
    14·2 answers
  • Can you help me with the answers
    11·1 answer
  • Is a triangle with side lengths 6, 10, 12 a right triangle?
    13·2 answers
  • What is the slope-intercept equation of the line below?
    5·2 answers
  • Express 593 million in scientific notation
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!