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
Vikentia [17]
3 years ago
15

A survey organization has used the methods of our class to construct an approximate 95% confidence interval for the mean annual

income of households in a county. The interval runs from $66,000 to $70,000 . If possible, find an approximate 99% confidence interval for the mean annual income of households in the county. If this is not possible, explain why not.
Mathematics
1 answer:
lawyer [7]3 years ago
7 0

Answer:

\bar X = \frac{66000+70000}{2}= 68000

We can estimate the margin of error with this formula:

ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000

And the margin of error is given by:

ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

And we can rewrite the margin of error like this:

ME =z_{\alpha/2}*SE

Where SE= \frac{\sigma}{\sqrt{n}}

For 95% of confidence the critical value is z_{\alpha/2}= \pm 1.96

The Standard error would be:

SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408

For 99% of confidence the critical value is z_{\alpha/2}= \pm 2.58

And the new margin of error would be:

ME = 2.58* 1020.408 = 2632.653

And then the interval would be given by:

Lower = 68000- 2632.653 = 65367.347

Upper = 68000+ 2632.653 = 70632.653

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".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

The 95% confidence interval is given by (66000 , 70000)

We can estimate the mean with this formula:

\bar X = \frac{66000+70000}{2}= 68000

We can estimate the margin of error with this formula:

ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000

And the margin of error is given by:

ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

And we can rewrite the margin of error like this:

ME =z_{\alpha/2}*SE

Where SE= \frac{\sigma}{\sqrt{n}}

For 95% of confidence the critical value is z_{\alpha/2}= \pm 1.96

The Standard error would be:

SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408

For 99% of confidence the critical value is z_{\alpha/2}= \pm 2.58

And the new margin of error would be:

ME = 2.58* 1020.408 = 2632.653

And then the interval would be given by:

Lower = 68000- 2632.653 = 65367.347

Upper = 68000+ 2632.653 = 70632.653

You might be interested in
What is the approximate distance from Denver to Chicago? Use a proportional relationship to solve the problem. Show your work.
Juli2301 [7.4K]

Answer:

d = 1002.6\,mi

Step-by-step explanation:

Approximately 5 units are equal to 557 miles and the scaled distance between Denver to Chicago is 9 units. The real distance can be estimated by simple rule of three:

d = \frac{9}{5}\times (557\,mi)

d = 1002.6\,mi

7 0
3 years ago
4+2(8²×4²)+6+4+6+6+6+2+2​
mash [69]

Answer: =2084

 

4+2(82)(42)+6+4+6+6+6+2+2

=4+264(42)+6+4+6+6+6+2+2

=4+2(64)(16)+6+4+6+6+6+2+2

=4+(2)(1024)+6+4+6+6+6+2+2

=4+2048+6+4+6+6+6+2+2

=2052+6+4+6+6+6+2+2

=2058+4+6+6+6+2+2

=2062+6+6+6+2+2

=2068+6+6+2+2

=2074+6+2+2

=2080+2+2

=2082+2

=2084

 

4 0
3 years ago
Read 2 more answers
Anna is covering the circular pool with a heavy-duty coer for the winter. The pool has a diameter of 24 feet. The cover extends
MrRa [10]
12 multiplied by 24.
7 0
3 years ago
Read 2 more answers
Please answer this question are you please
Mice21 [21]
It is too blurry to read it get a better camera
6 0
3 years ago
I WILL MARK AS BRAINLIEST!!!A man selling hot dogs, french fries, and a soda as a combo meal at a fairground has to pay the coun
9966 [12]

Answer:

C

Step-by-step explanation:

I think the answer is C, I am not 100% sure tho

5 0
3 years ago
Other questions:
  • One batch of walnut muffins uses 1 cups of walnuts. How many cups of
    6·1 answer
  • What is the solution to –30 + k = 9?
    15·2 answers
  • A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is wo
    8·1 answer
  • HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    14·1 answer
  • PLEASE HELP!!!
    12·1 answer
  • Please help with this question.
    7·1 answer
  • 5(10x +6) = ?
    15·2 answers
  • How to find the slope of x-y= -1 using y=mx+b?
    15·1 answer
  • Your final bill at the restaurant is $120 including a 20% tip. What was the cost of the original bill?
    9·2 answers
  • Domain and range of this graph
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!