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
kherson [118]
3 years ago
15

A random sample of 5120 permanent dwellings on an entire reservation showed that 1627 were traditional hogans.

Mathematics
1 answer:
krek1111 [17]3 years ago
8 0

Answer:

a) \hat p=\frac{1627}{5120}=0.3178

b)The 99% confidence interval would be given by (0.301;0.355)

Step-by-step explanation:

1) Notation and definitions

X=1627 number of permanent dwellings on the entire reservation that are traditional hogans.

n=5120 random sample taken

\hat p=\frac{1627}{5120}=0.318 estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.

p true population proportion of permanent dwellings on the entire reservation that are traditional hogans.

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}})

Part a

The point of estimate for p=the proportion of all permanent dwellings on the entire reservation that are traditional hogans is given by:

\hat p=\frac{1627}{5120}=0.3178

Part b

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:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

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

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

If we replace the values obtained we got:

0.318 - 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.301

0.318 + 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.335

The 99% confidence interval would be given by (0.301;0.355)

You might be interested in
Why does insurance often provide "peace of mind"?
snow_tiger [21]
If an item you own is damaged or stolen, insurance will give you money to replace it.
6 0
3 years ago
Read 2 more answers
Round to the nearest thousandth.<br> -49.5176
Oliga [24]

Answer:

-49.518

This should suffice.

7 0
2 years ago
Read 2 more answers
What is the volume of the following rectangular prism????help fast pleasee
Dmitrij [34]

Answer:

28/3

Step-by-step explanation:

3 0
3 years ago
I will give BRAINLIEST to whoever is correct.
attashe74 [19]
28/11.2 = 2.5

since they are similar and openly stated as parrallelograms, you know that they have a scale of the longest edge of EFGH to the longest edge of JKLM
5 0
3 years ago
Solve for x: 2 over 5 (x − 4) = 2x.<br><br> −8<br> negative 1 over 2<br> 1<br> −1
vlabodo [156]
2/5(x - 4) = 2x
2/5x - 8/5 = 2x....multiply everything by 5
2x - 8 = 10x
-8 = 10x - 2x
-8 = 8x
-8/8 = x
-1 = x <===
5 0
3 years ago
Other questions:
  • The cartoon can hold 1000 unit cubes I measured 1" x 1" x 1".Describe the dimensions of the carton using unit cubes
    9·1 answer
  • Which of the following can also be written as a recursive sequence?
    9·2 answers
  • I WILL GIVE BRAINLY AND 30 POINTS TO WHOEVER ANSWERS FIRST AND GETS THEM RIGHT
    13·2 answers
  • Luke has 48 books he puts 7 books in a box how many boxes can he fill?? Explain how you interpreted the remainder.
    7·2 answers
  • Are these equal or not equal?
    14·2 answers
  • 7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken
    5·1 answer
  • How do two different genres address a similar topic?
    14·1 answer
  • Can I get help on this one
    14·2 answers
  • Please HELP
    8·1 answer
  • Practice Rounding to the Nearest Ten<br> 37 rounds to
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!