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
HACTEHA [7]
3 years ago
11

Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying withi

n their school. They select a random sample of 200 students who are asked to complete a survey anonymously. Of these students, 63 report that they have experienced bullying. Use this information to find a 90% z-confidence interval for p, the true proportion of students at this school who have experienced bullying. Give the limits (bounds) of the confidence interval as a proportion, precise to three decimal places.
lower limit =______________

upper limit =___________
Mathematics
1 answer:
boyakko [2]3 years ago
5 0

Answer:

lower limit =0.261

upper limit =0.369

Step-by-step explanation:

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".  

Description in words of the parameter p

p represent the real population proportion of people that have experienced bullying

X= 63 people in the random sample that have experienced bullying

n=200 is the sample size required  

\hat p=\frac{63}{200}=0.315 represent the estimated proportion of people that have experienced bullying

z_{\alpha/2} represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Numerical estimate for p

In order to estimate a proportion we use this formula:

\hat p =\frac{X}{n} where X represent the number of people with a characteristic and n the total sample size selected.

\hat p=\frac{63}{200}=0.315 represent the estimated proportion of people that they were planning to pursue a graduate degree

Confidence interval

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 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.64  

And replacing into the confidence interval formula we got:  

0.315 - 1.64 \sqrt{\frac{0.315(1-0.315)}{200}}=0.261  

0.315 - 1.64 \sqrt{\frac{0.315(1-0.315)}{200}}=0.369  

And the 90% confidence interval would be given (0.261;0.369).  

We are confident at 90% that the true proportion of people that they were planning to pursue a graduate degree is between (0.261;0.369).  

lower limit =0.261

upper limit =0.369

You might be interested in
Pleaseeeeeeee help me
Juli2301 [7.4K]

Answer:

The answer is "The discriminant is positive"

Step-by-step explanation:

When the discriminant is positive there is two real solutions.

When the discriminant is equal to 0, there is one real solution.

When the discriminant is negative, there is no real number solutions.

8 0
3 years ago
Plzzzzz help me with this
ehidna [41]

Answer:

We conclude that we must add 4² or 16 to complete the square.

Hence, option C i.e. 16 is the correct answer.

Step-by-step explanation:

We know that the perfect square formula is

<em>(a + b)² = a² + b² + 2ab</em>

Given the equation

x^2+8x

Let us add 4² or 16 in the equation

x^2+8x+4^2

x^2+\:2\left(1\right)\left(4\right)x+4^2

as <em>(a + b)² = a² + b² + 2ab, </em>so

<em />x^2+8x+4^2=\left(x+4\right)^2<em />

<em />

Therefore, we conclude that we must add 4² or 16 to complete the square.

Hence, option C i.e. 16 is the correct answer.

4 0
3 years ago
Read 2 more answers
COMMON FACTOR QUESTION❌
Agata [3.3K]
The correct answer is D.
40/8=5 and 48/8=6
5 0
3 years ago
Read 2 more answers
Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her candy away, which amount of candy could have bee
True [87]
To find the answer to this problem, you just need to figure out which total amount of candy is divisible by 7.

161/7=23
<span>162/7=23.1428571429
</span>145/7=<span>20.7142857143
128/7=</span><span>18.2857142857

Obviously, Julie cannot give a fraction of an amount of candy to someone.  So that rules out that she had 162, 145, or 128 pieces of candy.  

The only amount of candies that Julie could have that is divisible by 7 is 161 candies, which means that 161 is your answer.</span>
5 0
3 years ago
Read 2 more answers
A ski slope drops 30 feet for every horizontal 70 feet
ASHA 777 [7]
The angle of depression is

tan^-1 3/7 = 23.2 deg
8 0
3 years ago
Other questions:
  • What is the exact of the expressions square root of 180 - square root of 125 + square root of 5
    5·1 answer
  • The average annual cost of the first year of owning and caring for a large dog is $1,843 (US News and World Report, September 9,
    6·1 answer
  • Simplify the following equation :
    8·1 answer
  • A recipe calls for 32 ounces of orange juice. How many cups of juice would you need for the recipe?
    11·2 answers
  • Help I am not that good with math so if anyone can help that would be great. Thank you
    12·1 answer
  • An aluminum can has a capacity of 2.37 L. What is the capacity of the can in milliliters?
    6·1 answer
  • Can someone help me please
    8·2 answers
  • Find the value of in the triangle shown below.<br> 13<br> 12<br> X
    8·1 answer
  • 12,000,055 + 60 + 16 + 90 x 40
    9·2 answers
  • Z(0,-5) Go left 5, up right, and down 3.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!