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
Snezhnost [94]
3 years ago
12

3 (a) A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confide

nce interval for the fraction of the voting population favoring the suit. (b) What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57
Mathematics
1 answer:
hammer [34]3 years ago
7 0

Answer:

a. 0.498 < p < 0.642

b. We are 96% sure that the error of estimator ^p = 0.57 will not exceed 0.07001

Step-by-step explanation:

Given;

Sample, n = 200 voters

Let x represent those that support annexation suit.

x = 114

First, we'll calculate the probability of supporting annexation suit.

Let p represent the probability of supporting annexation suit.

p = x/n

p = 114/200

p = 0.57

From elementary probability;

p + q = 1 where q represent probability of failure.

In this case, q represent probability of not supporting annexation suit

Substitute 0.57 for p

0.57 + q = 1

q = 1 - 0.57

q = 0.43

To find the 96% confidence interval for the fraction of the voting population favoring the suit;

The confidence interval is bounded by the following;

^p - z(α/2) √(pq/n) < p < ^p + z(α/2) √(pq/n)

At this point, we have values for p,q and n.

Next is to solve z(α/2)

First, we'll find the value of α/2 using

C.I = 100%(1 - α) where C.I = 96%

96% = 100%(1 - α)

1 - α = 96%

1 - α = 0.96

α = 1 - 0.96

α = 0.04

So,

α/2 = 0.04/2

α/2 = 0.02

So, z(α/2) = z(0.02)

Using normal probability table

z0.02 = 2.055 --- This is the closest value which leaves an area of 0.02 to the right and 0.98 to the left

Recalling our formula to solve 96% interval;

^p - z(α/2) √(pq/n) < p < ^p + z(α/2) √(pq/n)

By substituton, we have

0.57 - 2.055 * √(0.57*0.43/200) < p < 0.57 + 2.055 * √(0.57*0.43/200)

0.57 - 0.071939677073920 < p < 0.57 + 0.071939677073920

0.498060322926079 < p < 0.641939677073920 ---- Approximate

0.498 < p < 0.642

b. Here, we'll make use of the following theorem;

Using ^p as an estimate

We are 100%(1 - α) confident that the error will not exceed z(α/2) √(pq/n)

From (a), we have.

z(α/2) = 2.055, p = 0.57, q = 0.43, n = 200

By substituton, z(α/2) √(pq/n) becomes

2.055 * √(0.57 * 0.43/200)

= 2.055 * 0.071939677073920

= 0.070014284256857 ---- Approximate

= 0.07001

We are 96% sure that the error of estimator ^p = 0.57 will not exceed 0.07001

You might be interested in
The angels of a triangle have a sum of 180°. The angles of a rectangle have a sum of 360°. The angels of a pentagon have a sum o
Airida [17]

Step-by-step explanation:

It is given that the angels of a triangle have a sum of 180°. The angles of a rectangle have a sum of 360°. The angels of a pentagon have a sum of 540.

<u>Let me define the each terms.</u>

1. We know that each angle in a triangle is 60°, So there is a three angle in a regular triangle.

  • 60° + 60° + 60°
  • 180°

2. We know that each angle in a rectangle, is 90°, So there is a four angle in a regular rectangle.

  • 90° + 90°+90°+90°
  • 360°

Similarly,

  • There is 8 angle in a regular octagon and each angle measurement is 135°.

So, sum of the angles of an octagon = 135° × 8

Sum of the angles of an octagon = 1080°

Therefore, the required sum of the angles of an octagon is 1080°

6 0
3 years ago
Someone pls help im so close
Sliva [168]

Answer:  A) 126.6

<u>Step-by-step explanation:</u>

Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.

∠A + ∠B + ∠C = 180

∠A + 85 + 53 = 180

∠A + 138 = 180

∠A = 42

Now we have:

                       A = 42          B = 85       C = 53

                       a = 85          b = ???       c = ???

We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).

\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}

4 0
3 years ago
Find the length of the missing sides, round your answers to the nearest hundredth.
azamat
90 round to the nearest hundredth
5 0
3 years ago
We expect to see a line for a graph of a composition of a function and it's inverse function, if the domain of each is all _____
Helen [10]

The answer would be All (A)Real Numbers

4 0
3 years ago
RT and UW are parallel lines. Which angles are vertical angles? HELP ASAAPPP
MrRa [10]

Answer:

It is <uvx and <WVS..........

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which one describes the translation of f(x) to g(x) ?
    8·2 answers
  • Write each rational number as a terminating decimal.<br> 1. 19/20<br> 2. -1/8<br> 3. 17/5
    6·2 answers
  • Find the maximum and minimum values for the the graph of 7cos(x)
    14·1 answer
  • Property in equation. Find the value of n. 5+4= n+4
    9·1 answer
  • Divide Rs240 in the ratio 3:5
    9·1 answer
  • Last week you worked 24 hours, and earned $240.
    14·2 answers
  • Can someone help me, please and thank you? I'll give BRAINLEST to the person who gets it right!!! Please have explained how to g
    13·2 answers
  • Suppose the length of each side of a
    9·2 answers
  • Carlos made 32 of his 40 serve attempts over the net. What percent of his
    6·1 answer
  • You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!