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
Sever21 [200]
2 years ago
10

How large a sample n would you need to estimate p with margin of error 0.04 with 95% confidence? Assume that you don’t know anyt

hing about the value of p . 1037 256 601 423
Mathematics
1 answer:
BartSMP [9]2 years ago
3 0

Answer:

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

Since we don't know about p we can assume \hat p =0.5. And replacing into equation (b) the values from part a we got:  

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

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".  

\hat p estimation for the sample proportion

n sample size selected

Confidence =0.95 or 95%

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 values 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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical values would be given by:  

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96  

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 0.04 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 know about p we can assume \hat p =0.5. And replacing into equation (b) the values from part a we got:  

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

You might be interested in
Please help me answer this
ohaa [14]

i did the awnser is 173,668.18 there you goStep-by-step explanation:

6 0
2 years ago
A parking structure has three levels. There are 47 cars on the first level and 61 cars on the third level. How many cars are on
Anestetic [448]
54 I believe if this is what I think it is the end of the world as we see it the most hardest math riddle to have ever existed 61-47 = 14 
47+7=54  54+7= 61 therefore the world as we know shall come to a end at 2:08 PM Central time 
7 0
3 years ago
A file that is 256 megabytes is being downloaded. If the download is 17.3% complete, how many megabytes have been downloaded? Ro
dexar [7]
If i did my math right it should be 44.3
6 0
3 years ago
A table is going to be painted. How much less surface area of the table will be painted if the underside remains unpainted? leng
STALIN [3.7K]
440 will be remained out of 880
7 0
3 years ago
Read 2 more answers
What is a credit report? a. A credit report is a number representing your creditworthiness. b. A credit report is a detailed lis
zzz [600]

A credit report is a detailed listing of your credit history.

Answer: b

7 0
3 years ago
Read 2 more answers
Other questions:
  • If x2 + xy + y3 = 1, find the value of y''' at the point where x = 1.
    9·1 answer
  • 8) The equation of a line that has a slope of -2 and a y-intercept of 3 is:
    8·1 answer
  • Please help with number 1! Thanks
    14·1 answer
  • "Ten subtracted from the quotient of a number and<br>7 is less than -6.​
    13·1 answer
  • Marco starts getting ready for soccer practice at 3:55 P.M. if it takes him 15 minutes to get ready, what time is he ready to le
    9·1 answer
  • Catherine is using a spool of yarn to knit some items. She uses 14 3/8 yards of yarn to knit a scarf. The number of yards of yar
    10·2 answers
  • SOMEONE HELPPPPPPPPPP
    8·2 answers
  • Please solve this and show your work, I'll give Brainliest!<br> Please?
    15·1 answer
  • Stan wants to start an IRA that will have $250,000 in it when he retires in 25 years. How much should he invest semiannually in
    15·1 answer
  • HELP! DUE IN 5 MINS TvT
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!