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
grandymaker [24]
3 years ago
7

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

e local dealer. The customer relations department will survey a random sample of customers and compute a 96% confidence interval for the proportion who are not satisfied.(a) Past studies suggest that this proportion will be about 0.19. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.02.(You will need a critical value accurate to at least 4 decimal places.)Sample size:________(b) Using the sample size above, when the sample is actually contacted, 21% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?MoE: ________
Mathematics
1 answer:
monitta3 years ago
3 0

Answer:

a) n =1623

b) ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208    

Step-by-step explanation:

1) Notation and definitions

n random sample taken

\hat p=0.19 estimated proportion of customers are not satisfied with the service provided by the local dealer

Confidence =0.96 or 96%

Me= 0.02 represent the margin of error

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{p(1-p)}{n}})

Part a

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 96% of confidence, our significance level would be given by \alpha=1-0.96=0.04 and \alpha/2 =0.02. And the critical value would be given by:

z_{\alpha/2}=-2.0538, z_{1-\alpha/2}=2.0538

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 0.02 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{0.19(1-0.19)}{(\frac{0.02}{2.0538})^2}=1622.912  

And rounded up we have that n=1623

Part b

The margin of error is given by:

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    

So then if w replace the value of n obtained from part a we got:

ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208    

You might be interested in
Name<br> Add and Subtract Integers<br> Solve.<br> 1.-2+9
Rudiy27
Answer would be 7 since 2 is a negative you would subtract it from 9
7 0
3 years ago
Read 2 more answers
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy
slamgirl [31]

Answer:

20'×15 in 54 inches

Step-by-step explanation:

The Best as a pool should be rectangular in shape and 54inches deep for safety of life's

7 0
3 years ago
What is 940 divided by 58 please help I'm doing my brothers homework xD
erica [24]
16 with the remainder 2
3 0
3 years ago
Read 2 more answers
What is One + One?????????
pychu [463]

Answer:

one plus one is two the answer is 2

4 0
3 years ago
Read 2 more answers
Andre and Ronnie used a stopwatch to record the amount of time it took a golf ball to roll down a three-story ramp. Andre's ball
iren [92.7K]

Answer:

The answer would be A

Step-by-step explanation:

This is because when you take 1.625 it rounds back to 6 because 2 isnt more then 5 or 5 so it wouldn't round just like 1.635. I believe thats the answer im not positive

5 0
3 years ago
Read 2 more answers
Other questions:
  • The line graph below shows how Fergus has done on the first five vocabulary quizzes of the semester. What was Fergus's second-hi
    11·1 answer
  • of the 400 vehicles that passed the intersection, 98 are buses, what percent of the vehicles that passed the intersection are bu
    13·1 answer
  • Please answer it now in two minutes
    5·2 answers
  • What is the inverse of the function f(x) = 4x + 8?
    10·2 answers
  • If a+b= -1 then the value of a^3+b^3 - 3ab= ?
    9·1 answer
  • Solve using substitution
    9·1 answer
  • Is anyone else airpods not working like one ear not work and the case not charging​
    6·2 answers
  • Math Questions!!! Please help if you see this!!
    6·1 answer
  • A club decides to sell T-Shirts for $12 each as a fundraiser. It costs $20, plus $6 per T-shirt to make the T-shirts. Write and
    14·1 answer
  • PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE BRAINLY
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!