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
A furniture store salesman had $15,200 in total monthly sales last month. He made $912 in commission from those sales.
tatyana61 [14]
We need to find out what percentage $912 is of $15 200. The answer is 6%, if I'm understanding the question correctly.
8 0
3 years ago
Read 2 more answers
Can you tell what the graph of a line will look like without finding points or graphing it?
Anna71 [15]

Answer:

Yes. Use a chart to calculate the equation set and you will be able to determine the slope of such graph.

Step-by-step explanation:

5 0
3 years ago
Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and th
Oksana_A [137]

If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.

Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.

We know that speed is the distance covered by an object in a particular period of time.

Speed=distance/time.

It is expressed as kilometers per hour or miles per hour, etc.

If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.

Distance=45 miles.

Time =distance/speed

=45/30

=1.5

Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.

Learn more about speed at brainly.com/question/4931057

#SPJ4

8 0
1 year ago
How much grain can this container hold?
ludmilkaskok [199]

Answer:

953.78 in^3 of grain.

Step-by-step explanation:

The volume of a cylinder = π r^2 h.

For this cylinder r =  radius of the base = 9/2

= 4.5 in  and the height h = 15 in

So the volume is 3.14 * 4.5^2 * 15

= 953.78 in^3.

8 0
3 years ago
Read 2 more answers
Sally Jones had a policy with a $250 deductible which paid 80% of her covered charges less
weqwewe [10]

Answer:

50,,

Step-by-step explanation:

so you take 80percent of 250,, and deduct from medical expenses which becomes 50

4 0
2 years ago
Other questions:
  • Find the endpoint of segment CD if D(-3, 1/2) and the midpoint is (-1/2, 3).
    15·1 answer
  • Can you help answer this question
    13·1 answer
  • An aluminum rod 0.500 m in length and with a cross-sectional area of 2.20 cm2 is inserted into a thermally insulated vessel cont
    12·1 answer
  • Neena is listening to a song. It has a consistent beat. She counts 11 beats in
    15·1 answer
  • PLEASE PLEASE PLEASE HELP grade 9 work!!!!
    5·1 answer
  • Simplify: -8x +7-5-5x + 5x<br> A<br> - 8x + 2<br> B<br> -18x+12<br> -x-5<br> D<br> -X+12
    8·1 answer
  • Answer please !!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!
    12·2 answers
  • 7x-3=7x+5 no solution answer and steps ​
    6·2 answers
  • 3 to the second power x 3 x 3 x 3= <br><br> Simplified into exponential form
    6·2 answers
  • How to find the domain of a v-shaped graph?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!