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
MariettaO [177]
3 years ago
13

A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random samp

le of 35 homeowners. They find a 95% confidence interval for the true mean current debt to be ($56,000, $120,000). Which of the following would correctly produce a confidence interval with a smaller margin of error than this 95% confidence interval?
a. Using the balances of older homeowners because they will have paid off more of their mortgage
b. Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error
c. Using the balances of only fifteen homeowners rather than 35, because there is likely to be less variation in fifteen balances than 35
d. Using 99% confidence, because then its more likely that the true mean is contained in the confidence interval
Mathematics
1 answer:
Nat2105 [25]3 years ago
5 0

Answer:

b. Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

95% confidence interval

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

99% confidence interval

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find we find the width of our confidence interval M as such

M = z*\frac{\sigma}{\sqrt{n}}

So, as n increases, the width of the confidence interval decreases.

From the examples above, we can also conclude that as the confidence level increases, so does the value of z, which means that the width of the interval increases.

Which of the following would correctly produce a confidence interval with a smaller margin of error than this 95% confidence interval?

For a smaller margin of error, we need to have a bigger sample size.

So the correct answer is:

b. Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error

You might be interested in
If a is an integer, prove that (14a + 3, 21a + 4) = 1.
Firdavs [7]

Answer:

(14a+3, 21+4) = 1

Step-by-step explanation:

We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.

gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1

Therefore,

(14a + 3, 21a + 4) = 1

8 0
3 years ago
(5+22) x (35-27) + 6^2
aksik [14]
What does ^ stand for?
7 0
3 years ago
Can someone pls help me
Agata [3.3K]

Answer:

A triangle

Step-by-step explanation:

Please mark me as brainliest

6 0
3 years ago
Its like a word question?
Sloan [31]

Answer:

-3+x=x+4

Step-by-step explanation:

Pls Mark Brainliest

5 0
3 years ago
Read 2 more answers
Lucy and Emily are racing with each other and Lucy is 90
Zina [86]

Using the <em>system of equation</em> created, Emily will catch up Lucy after 30 seconds

Given the Parameters :

  • Lucy's distance = 2t
  • Emily's distance = 5t

<u>We can set up an equation to represent the required scenario thus</u> :

Emily's distance = Lucy's distance + 90

5t = 2t + 90

We solve for t

<em>Collect like terms</em> :

5t - 2t = 90

3t = 90

Divide both sides by 3 to isolate t

t = 90/3

t = 30

Therefore, Emily will catch up with Lucy after 30 seconds

Learn more :brainly.com/question/13218948

8 0
2 years ago
Other questions:
  • Which expression has the least value when x=100 <br><br> a. 1/x<br> b. 10/x<br> c. 1-x<br> d. 10-x
    10·2 answers
  • Is 3x+2y=6 the standard form of y = 3/2 x +3<br> EXPLAIN WHY
    15·2 answers
  • How can you use addition to find the distance between 4 and 7
    5·1 answer
  • many credit card companies charge a compound interest of 1.8% per month on a credit card balance. Miriam owes 750 on a credit ca
    10·2 answers
  • What are some abundant numbers
    10·1 answer
  • Solve -2a-5&gt;3. which graph shows the solutions?<br>​
    15·1 answer
  • Which expression is equal to (x+2)(x−4)(x−4)(x+4)?
    15·1 answer
  • Three more than the quotient of a number and 7 is at most 92. Find the number
    9·1 answer
  • Wave hits an object as shown.
    12·2 answers
  • vijay is building a new rectangular enclosure in his backyard for his chickens. he has 404040 feet of fencing material and he wa
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!