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
schepotkina [342]
2 years ago
14

A random sample of n 1 = 249 people who live in a city were selected and 87 identified as a democrat. a random sample of n 2 = 1

13 people who live in a rural area were selected and 58 identified as a democrat. find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a democrat and the proportion of people that live in a rural area who identify as a democrat.
Mathematics
1 answer:
kvasek [131]2 years ago
5 0

Answer:

CI=\{-0.2941,-0.0337\}

Step-by-step explanation:

Assuming conditions are met, the formula for a confidence interval (CI) for the difference between two population proportions is \displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2} where \hat{p}_1 and n_1 are the sample proportion and sample size of the first sample, and \hat{p}_2 and n_2 are the sample proportion and sample size of the second sample.

We see that \hat{p}_1=\frac{87}{249}\approx0.3494 and \hat{p}_2=\frac{58}{113}\approx0.5133. We also know that a 98% confidence level corresponds to a critical value of z^*=2.33, so we can plug these values into the formula to get our desired confidence interval:

\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\CI=\biggr(\frac{87}{249}-\frac{58}{113}\biggr)\pm 2.33\sqrt{\frac{\frac{87}{249}(1-\frac{87}{249})}{249}+\frac{\frac{58}{113}(1-\frac{58}{113})}{113}}\\\\CI=\{-0.2941,-0.0337\}

Hence, we are 98% confident that the true difference in the proportion of people that live in a city who identify as a democrat and the proportion of people that live in a rural area who identify as a democrat is contained within the interval {-0.2941,-0.0337}

The 98% confidence interval also suggests that it may be more likely that identified democrats in a rural area have a greater proportion than identified democrats in a city since the differences in the interval are less than 0.

You might be interested in
Need math help for this
Burka [1]

Answer:

<h2>In the attachment</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

m - slope

(x₁, y₁) - point

We have the equation:

y-5=-\dfrac{2}{3}(x+9)\\\\y-5=-\dfrac{2}{3}(x-(-9))

Therefore we have

the slope m = -2/3

and the point (-9, 5)

A slope

m=\dfrac{rise}{run}

rise = -2

run = 3

From the point (-9, 5) ⇒ 2 units down and 3 units to the right.

7 0
3 years ago
How many solutions are there to
Alika [10]

Answer:

C

Step-by-step explanation:

there are infinitely many solutions since different values of x and y will work for this simultaneous equation

8 0
3 years ago
If 2 is a factor of a number, is that number a prime number? <br><br> ___________ explain
Nataliya [291]
Yes it is. It is the only even number that is prime that is multiplied by 1.
4 0
3 years ago
Solve. −35x+15&gt;720 Drag and drop a number or symbol into each box to show the solution.
vampirchik [111]

Answer:

The solution of the inequality - 35x + 15 > 720  is x

Step-by-step explanation:

Consider the given inequality

- 35x + 15 > 720

Subtract both side by 15 , we get

- 35x + 15 - 15 > 720 - 15

- 35x > 705

Multiply both sides by -1 (Reverse the inequality )

(-35x)(-1) < 705 (-1)

35x < -705

Now, divide both side by 35

\frac{35x}{35}=\frac{-705}{35}

\Rightarrow x=\frac{-141}{7}

Thus, the solution of the inequality - 35x + 15 > 720  is x

6 0
3 years ago
Angle ABC is formed by segments AB and BC on the following coordinate grid: A coordinate grid is shown from positive 6 to negati
Nadusha1986 [10]

Answer:

B) m∠ A'B'C' = m∠ABC

Step-by-step explanation:

A rotation does not change angle measure or side length.  It preserves congruence.

This means that the image angle, A'B'C', will be congruent to the pre-image angle, ABC.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Mary, who is 4 feet tall, casts a shadow 2 feet long. At the same time, a pole casts a shadow 3 feet long. How tall is the pole?
    11·1 answer
  • Find the number of distinguishable permutations for the word MAGNETIC
    11·1 answer
  • You have 15 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 20 g
    14·2 answers
  • What value is equivalent to 8 · 9 − 2 · 5? A) 62 B) 82 C) 280 D) 350
    8·2 answers
  • Is 1.1 bigger than 0.7
    15·2 answers
  • Someone help please.
    15·1 answer
  • Cindy earned $618.00 on her last paycheck. Two-thirds of what she earned was commission, How much did Cindy earn in commission o
    11·1 answer
  • A +1&gt;3<br>guyz at least solve one question ​
    12·1 answer
  • -8=-5+x+9 what are the steps to this equation?
    9·1 answer
  • HELP PLEASE ASAP WILL GIVE BRAINLIEST
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!