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
Stels [109]
3 years ago
10

The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,

they calculate that average sale price for their 15 listings is 400.
(a) Given that the standard deviation of sale prices is known to be 80, calculate a 99 percent confidence interval for the average sale price in Guelph.
(b) Given that the standard deviation of sale prices is unknown but estimated to be 80, calculate a 99 percent confidence interval for the average sale price in Guelph.
Mathematics
1 answer:
strojnjashka [21]3 years ago
4 0

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) 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=400 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=80 represent the population standard deviation

n=15 represent the sample size  

2) Part a

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

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

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

400-2.58\frac{80}{\sqrt{15}}=346.708    

400+2.58\frac{80}{\sqrt{15}}=453.292

So on this case the 99% confidence interval would be given by (346.708;453.292)    

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that t_{\alpha/2}=2.98

Now we have everything in order to replace into formula (1):

400-2.98\frac{80}{\sqrt{15}}=338.445    

400+2.98\frac{80}{\sqrt{15}}=461.555

So on this case the 99% confidence interval would be given by (338.445;461.555)    

You might be interested in
there were 630 tickets sold. each ticket cost $21. how much money was raised from selling the .tickets
Orlov [11]
The amount of money made was $13,230.
7 0
3 years ago
Read 2 more answers
Statistics :Q6..........
scZoUnD [109]
I’m thinking A. Would be the most suitable answer for this one
7 0
3 years ago
Read 2 more answers
What is Pythagorean triples​
Georgia [21]

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
7 0
2 years ago
Read 2 more answers
Anita purchased a couch that was priced at $700. She will also have to pay 6% sales tax. How much will she pay in total for the
Zolol [24]

Answer:

$742

Step-by-step explanation:

To solve this, you need to figure out what 6% of 700 dollars is and then add that to 700. The easiest way to find the percentage of a number is to set it up in the equation:

6/100 = x/700  where 6 is the percentage of 700 (out of 100 because you can only get up to 100 percent in this case) and x is 6 percent of 700. when you cross multiply, you get 100x = 4200. Then you divide both sides by 100 to get x by itself. This will give you x = 42 Add this to 700 for 742 as the total amount that will be paid. Sorry if this first half was a little confusing

6 0
3 years ago
First person gets brainliest lol
fgiga [73]

Answer:

YAY

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is (3x9-6+3\10)
    12·1 answer
  • When calculating the volume of an object, why do the units end up being raised to the third power as in cm3?
    5·1 answer
  • How many fluid ounces equal 47 gallons
    5·2 answers
  • The Melt in Your Mouth Chocolate Factory opens its doors each day at 7:00 am sharp. Sally arrived at the factory 10 minutes befo
    7·1 answer
  • Find x to the nearest tenth. Click on the pic i really need help
    8·1 answer
  • A rental car company charges $77.25 per day to rent a car and $0.12 for every mile
    6·1 answer
  • Im having a mental breakdown HELPPPP!​
    9·1 answer
  • Plz help!!! will give 20 points
    7·2 answers
  • X+y=8 solve by substitution <br> and<br> Y=3x with substitution too
    9·1 answer
  • What is a greatest common factor (gcf)? find the gcf for the expression 3x^2 + 9x
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!