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
Artist 52 [7]
3 years ago
9

In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system

to a semester-system. How many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval
Mathematics
1 answer:
Contact [7]3 years ago
3 0

Answer:

n=206

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".  

The population proportion have the following distribution

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

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:

t_{\alpha/2}=-2.58, t_{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 0.09, we can use as prior estimate of p 0.5, since we don't have any other info provided, 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{0.09}{2.58})^2}=205.44  

And rounded up we have that n=206

You might be interested in
A police officer estimated the distance from one side of a street to the other to be 14m . The actual distance was 13.4.
Oksi-84 [34.3K]
The absolute error is 0.2 and the percent error is 1.45 I hope this helps
7 0
3 years ago
Can you divide 25 into 4 equal groups? Explain why or why not.
alexira [117]

Answer:

No, not really.

dividing 25 into 4 equal groups, equals 6.25.

So no, you can not divide 25 into 4 equal group.

If if was 25 into 5 equal groups, then yes.

Hope this helps!!!

Please mark brainliest, if this helps. :)

Step-by-step explanation:

8 0
3 years ago
Select the correct answer from each drop-down menu.
mixer [17]

Answer:

1. Different

2. More

3. Greater too

Step-by-step explanation:

I'm not completely sure I'm not good with graphs but i hope its right!

5 0
2 years ago
How many meters is 1/2 decameter
trapecia [35]

Answer: 5 meters

Step-by-step explanation: 1/2 = .5, if you move the decimal in front of the 5, you would go from .5 to 5

3 0
3 years ago
Scientist A dissolved 1.0 kilogram of salt in 3.0 liters of water. Scientist B dissolved 20 pounds of salt in 7.0 pints of water
Lilit [14]

scientist A dissolved 1 kg of salt in 3 litres.

scientist B dissolved 20 pounds of slat in 7 pint of water.

we know that 1 pound =0.543 g

20 pounds=9.07 kg.

1 pint=0.5 litres

so 7 pints =3.5 litres

so dissoving 1 kg of salt in 3 litres of water and 9.07 kg in 3.5 litres of water

we know that for concentration kg/l units is used .

for A= 1/3=0.33kg/l

and B=9.07/3.5=2.59 kg/l.

so scientist A has prepared more concentrated solution .

3 0
2 years ago
Read 2 more answers
Other questions:
  • Use partial quotient 28 divided by 514
    12·1 answer
  • What is the meaning of the prefix super-? to or toward before together with over or above
    6·2 answers
  • In this picture B and F are midpoints.
    12·1 answer
  • Whats the percent change from 100 to 140​
    10·1 answer
  • Which number expression represents 1/2 the sum of 7 and 5 please help
    7·1 answer
  • Write a rule for the nth term of the sequence.
    7·1 answer
  • Suppose a number cube is rolled twice. What is yhe probability that an odd number will show both times?
    9·1 answer
  • Monica and jaimy are creating number patterns. Monica uses the rule . "Multiply by 3 and stats at 4 .Jaimy uses the rule "add 6
    6·1 answer
  • 2x - 5y = 6 and -2x + 7y = 14 <br><br>*Using elimination*​
    13·2 answers
  • If you are choosing a single card from a standard deck of playing cards, what is
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!