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Complete Question

How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?

Exercise 9.53

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

Answer:

The First question

                    [tex] n = 1879  [/tex]

A

    The 96% confidence interval is  

                      [tex]0.51 <  p <  0.63 [/tex]

B

   The possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is  

           [tex]E =    0.06 [/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]E = 0.02[/tex]

     The sample size is  n =  200

     The number that supported the annexation suit is  k = 114

Considering the first question

Generally our sample in Exercise 9.53 is  [tex]\^ p = 0.57[/tex]

From the question we are told the confidence level is  96% , hence the level of significance is    

      [tex]\alpha = (100 - 96 ) \%[/tex]

=>   [tex]\alpha = 0.04[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.751 [/tex]

Generally the sample size is mathematically represented as  

    [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]

=>  [tex]n = [\frac{1.751}{0.02 } ]^2 * \^ p (1 - \^ p ) [/tex]

=>  [tex]n = [\frac{1.751}{0.02 } ]^2 * 0.57  (1 -0.57  ) [/tex]

=>  [tex] n = 1879  [/tex]

Considering question B

Generally the margin of error is mathematically represented as  

     [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]

=>  [tex]E =    1.751 * \sqrt{\frac{ 0.57  (1- 0.57 )}{200} } [/tex]

=>  [tex]E =    0.06 [/tex]

Considering question A

Generally the sample proportion of the number that supported the annexation suit is mathematically represented as

        [tex]\^ p = \frac{114}{200}[/tex]

=>      [tex]\^ p = 0.57[/tex]

Generally 96% confidence interval is mathematically represented as  

      [tex]\^ p -E <  p <  \^ p +E[/tex]

=>  [tex]0.57  - 0.06 <  p <  0.57  + 0.06 [/tex]

=>  [tex]0.51 <  p <  0.63 [/tex]

Answer:

BROOO I LITERALLY HAD A WHOLE LOOOONG ANSWER AND SOME STU PID MOD CAME AND DELETED IT AND I DONT REMEMBER WHAT I PUT

Step-by-step explanation:

Answer:

a. 1/3x+6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

PEMDAS

First we do the parenthesis, then we multiply and then we subtract (left to right)

= (2+2) * 3 - 1 - 4

= 4 * 3 - 1 -4

= 12 - 1 -4

= 12

Answer:

15309 Im pretty sure

Step-by-step explanation:

a7=ar^7

=7(3^7)

7 x 2187=15309

Answer:

I think is c 2 hope that works

Step-by-step explanation:

please give brainliest :D

Answer:

First, find the common difference for the sequence. Subtract the first term from the second term. Subtract the second term from the third term. Subtract the third term from the fourth term. To find the next value, add to the last given number.

Step-by-step explanation:

Answer:

The appropriate response is "(26.03, 33.97)".

Step-by-step explanation:

The given values are:

Average maternal age,

[tex]\bar{x} = 30[/tex]

Standard deviation,

s = 6.2

Random sample,

n = 20

Now,

The degree of freedom will be:

⇒ [tex]df=n-1[/tex]

        [tex]=20-1[/tex]

        [tex]=19[/tex]

"t" at confidence level 99%, will be:

⇒ [tex]\alpha=1-99 \ percent[/tex]

       [tex]=1-0.99[/tex]

       [tex]=0.01[/tex]

⇒ [tex]\frac{\alpha}{2}=\frac{0.01}{2}[/tex]

       [tex]=0.005[/tex]

⇒ [tex]t\frac{\alpha}{2} \ df=t \ 0.005,19[/tex]

By using the student table, we get

             [tex]=2.86 1[/tex]

The margin of error will be:

⇒ [tex]E=\frac{t \alpha}{2,df\times (\frac{s}{\sqrt{n}})}[/tex]

On substituting the estimated values, we get

⇒     [tex]=2.861\times (\frac{6.2}{\sqrt{20}})[/tex]

⇒     [tex]=3.97[/tex]

At 99%, the confidence level will be:

⇒ [tex]\bar{x}-E< \mu <\bar{x}+E[/tex]

⇒ [tex]30-3.97< \mu < 30+3.97[/tex]

⇒ [tex](26.03,33.97)[/tex]

Thus the above is the correct approach.

Answer:

u may need a calculator

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

First, subtract 7 from both sides to get x alone. That will give you 4x = 24 .

Then divide both sides by 4 to remove the coefficient of x. That means x = 6.

4x+7=31

    -7   -7

4x=24

÷4   ÷4

x  =  6

9514 1404 393

Answer:

  78

Step-by-step explanation:

The base (JL) is twice the length of the midline (MN), so you have ...

  4x +34 = 2(5x -16)

  4x +34 = 10x -32 . . . eliminate parentheses

  66 = 6x . . . . . . . . add 32-4x

  11 = x

Then the length of JL is ...

  4(11) +34 = 78

Answer:

15

Step-by-step explanation:

2

4

6

8

10

there are 5 between 1-10

so 3*5=15 between 1-30

Answer:

15

Step-by-step explanation:

my head hurts too

Answer:

b

Step-by-step explanation:

Answer:

1.5 or 3/2

Step-by-step explanation:

The division results the quotient is 1.5

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication. In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items.

Given:

We have to divide 12.645 by 8.43

So,   12.645/8.43

= 12645/ 8430

=           8430 | 12645   | 1 . 5

                         8430

                      -______

                          42150

                          42150

                         _______

                               0  

Hence, the quotient is 1.5.

Learn more about division here:

https://brainly.com/question/21416852

#SPJ5                        

Part 1:

Answer:36 red beads

Step-by-step explanation:

12/4=3 beads per bracelet

3x12=36 red beads

Part 2:

Answer:48 red beads

Explanation:

We know 3 red beads per bracelet.

3x16=48 red beads

Answer:

The value of AC = 5 units

Step-by-step explanation:

Given the triangles

In the diagram,

We know that two triangles are termed as similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Therefore,

AB : XY = AC : XZ

AB / XY  = AC / XZ

as

so we can determine AC as the ratios of the side become

4 / 6  = AC / 7.5

AC = 4/6 × 7.5

      = 5 units

Therefore, the value of AC = 5 units

Answer:

-12.50x+350<210

Step-by-step explanation:

Answer: About 17 hours

Step-by-step explanation:

1,203/70=17.18571429

17.18571429 is about 17 hours

Answer: 2cm/year

Step-by-step explanation:

1m = 100cm

200m = 20000cm

10,000years = 20,000cm

1 year = 20,000/10,000 = 2cm

It's rate is 2cm/year

Answer:

0.02 cm/year

Step-by-step explanation:

200m:10,000 years

10,000 divided by 10,000=1

200 divided by 10,000=0.02

0.02m : 1 year

Best,

SunflowerJada

Answer:

she received 21 more

Step-by-step explanation:

43 + 34 =77

98-77= 21

Hope this helps!!!

Answer:

since i dont have data this is the best i can do

Step-by-step explanation:

non-filled seats diveded by total number of seats, everything multilped by 100 gives you percentage of non-filled seats.

Filled seats diveded by total number of seats, everything multilped by 100 gives you percentage of filled seats.

total should add up to 100

Answer:

B

Step-by-step explanation:

multiple 12 and 120 which is 1,440 then multiply 4 and 30 which is 120 and add it up which comes to 1,560. HOPE THIS HELP!!!

The total number of adults tickets sold and children tickets sold is 120 adult tickets and 30 children's tickets

Given:

Cost of adult tickets = $12

Cost of children tickets = $4

let

number of children tickets sold = x

number of adult tickets = 4x

Total cost of tickets = 1560

The equation:

1560 = 12(4x) + 4(x)

1560 = 48x + 4x

1560 = 52x

divide both sides by 52

x= 1560/52

x = 30

Therefore,

number of children tickets sold = x

= 30 tickets

number of adult tickets = 4x

= 4(30)

= 120 tickets

Read more:

https://brainly.com/question/15165519

Answer:

Answer Choice B

Step-by-step explanation:

f(x) is just another way of saying y=.

To inverse, just flip the x & y and isolate the y variable.

[tex]x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9}=y[/tex]

Answer:

The probability of not picking a pink jelly bean: 11/15    

Step-by-step explanation:

As we know that the maximum value of the probability of an event would always be 1.

Given that the probability of picking a pink jelly bean out of a bag is 4/15.

Thus, the probability of not picking a pink jelly bean can be calculated by subtracting 4/15 from the maximum probability '1'.

i.e.

Probability of not picking a pink jelly bean = max probability - 4/15

                                                                       = 1 - 4/15

                                                                      = 11/15

Therefore, the probability of not picking a pink jelly bean: 11/15                                                                    

Answer:

its either 98 cm or 28 cm

Step-by-step explanation:

7 x 7 = 49 x 2 = 98 cm

14 x 2 = 28

Answer:

9.

Step-by-step explanation:

Answer:

3 miles in 24 minutes

Step-by-step explanation:

Answer:

Sale Tax($): 4.5

Step-by-step explanation:

Before Tax Price ($):  72

Tax Rate (%): 6.2

Final Price Including Tax ($):  76.46

Sale Tax($): 4.46

Answer:

76.46

Step-by-step explanation:

Answer:

6.71

Step-by-step explanation:

If you want to put picture i would recommend using your phone to do it. :]

Answer: its 6.71

Step-by-step explanation: