A certain forum reported that in a survey of 2005 american adults, 27% said that they believe in astrology.
(a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.) Interpret the resulting interval.
i. We are 99% confident that the true population mean lies below this interval.
ii. We are 99% confident that the true population mean lies above this interval.
iii. We are 99% confident that this interval contains the true population mean.
iv. We are 99% confident that this interval does not contain the true population mean.
(b) what sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p? Round your answer up to the nearest integer.)

Answers

Answer 1

Answer:

               

Step-by-step explanation:

                 

Answer 2

Using confidence interval concepts, it is found that:

a)

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

The interpretation is:

iii. We are 99% confident that this interval contains the true population mean.

b)

A sample size of 664 would be required.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm M[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].

The interpretation of a x% confidence interval between a and b is that we are x% confidence that the true population mean lies in this interval, thus, option iii is correct.

In this problem:

Survey of 2005 adults, thus [tex]n = 2005[/tex].27% believe in astrology, thus, [tex]p = 0.27[/tex].99% confidence interval, thus z has a p-value of [tex]\frac{1 + 0.99}{2} = 0.995[/tex], thus z = 2.575.

Then:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 2.575\sqrt{\frac{0.27(0.73)}{2005}}[/tex]

[tex]M = 0.026[/tex]

The interval is:

[tex]M - \pi = 0.27 - 0.026 = 0.244[/tex]

[tex]M + \pi = 0.27 + 0.026 = 0.296[/tex]

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

Item b:

Irrespective of the value of p, thus [tex]\pi = 0.5[/tex].Margin of error of [tex]M = 0.05[/tex], and we have to find n:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 2.575(0.5)[/tex]

Dividing both sides by 0.05.

[tex]\sqrt{n} = 2.575(10)[/tex]

[tex](\sqrt{n})^2 = [2.575(10)]^2[/tex]

[tex]n = 663.1[/tex]

Rounding up:

A sample size of 664 would be required.

A similar problem is given at https://brainly.com/question/16807970


Related Questions

What are the solutions of x2 - 7x + 13 = 0 ? Imaginary numbers

Answers

Answer:

Step-by-step explanation:

I know what your thinking YOU DIDNT ANSWER!!!!! but think again i did, it is just an imaginary answer. dad jokeCRINGE!!!!!

Answer:

2 imaginary numbers

Step-by-step explanation:

x^2-7x+13=0

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40 points! Please help me

Answers

Answer:

x = 8

y = 14

Step-by-step explanation:

2x + 6 = 4x - 10 (Corresponding angles so they're equal)

2x - 4x = -10 - 6

-2x = -16

x = 8

2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)

2(8) + 6 + 13y - 24 = 180

16 + 6 + 13y - 24 = 180

13y - 2 = 180

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Answer:

2x+6=4x-10[corresponding angle]

16=2x

x=8

again

2×8+6+13y-24=180°[linear pair]

13y=180+2

y=182/13

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Answer:

2

Step-by-step explanation:

1 + 1 = 2

Number Order: 1 2 3 4 5 6...

1 plus an additional value of 1 gives us the next number which is 2

Which function is best represented by this graph?

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Answer:

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Step-by-step explanation:

Answer:

B

Step-by-step explanation:

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Please help 30 points pls

Answers

Answer:

4.75b; 8

Step-by-step explanation:

Area of triangle: height ÷ 2 × base

38 = 9.5 ÷ 2 × b

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38 = 4.75b

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b = 8

Answer:

4.75 & 8

Step-by-step explanation:

Hope this helps

Juice is on sale with the rule "buy one, get one half-off.” Write an expression two different ways to represent the cost of buying two containers of juice, j, on sale. Enter the correct answers in the boxes. ​

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Answer:

34

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2/5 of 16= (estimate each product)

Answers

Answer:

6.4 rounds down to 6.

Step-by-step explanation:

Divide 16 by 5. Multiply that number by 2.

Hank has 4 green marbles for every 9 red marbles. If hank has 39 total marbles, how many green marbles does he have? pls answer ASAP it for assignment

Answers

He has 12 green marbles. 4+9=13 and 39/13=3 so 4x3=12. to check, we can do 9x3=27 as well and add our results. 12+27=39 so we know we are correct.

Answer:

12 green marbles

Step-by-step explanation:

in this case we have to add the the green marbles as 4 and red marbles as 9

so, 4 + 9 = 13 and divide the total marbles to it

so, 39/13 = 3

so, here we have 3 times marble in 13 green marble to get the total number

so, 3 (13)

so, in this case we have to separate the green and red

so, 13 as ( 9 red + 4 green)

so,3 times  ( 9 red + 4 green)

in this case we can use distributive property of multiplication

so, 3 times 9 red = 27 is the total red marbles

and 3 times 4 green = 12 is the total green marbles

to check the answer we have to add this two

so, 27 red marbles + 12 green marbles = 39 total marbles

so, that's why it is 12 green marbles

Please mark me as brainliest

A company's human resources department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: Based on the values of the arithmetic mean, median, and mode, what is the most likely shape of the distribution

Answers

Answer:

hello your question is incomplete  below is the complete question

A company's human resources department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: 12 16 18 19,21 21, 21,22 24 24 26What is the arithmetic mean, median and mode? what is the most likely shape of the distribution

answer :

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ii) median = 21

iii) mode = 21

iv) The most likely shape is a Bell - shaped curve

Step-by-step explanation:

sample size = 11

values ( observations ) = 12, 16, 18, 19,21,21,21,22,24,24,26

i) mean

 = ∑ values / sample size = 224 / 11 = 20.36

ii) median

median is the value of the data located at the center of the string of data

to determine the middle position = ( n+1 / 2 )

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What is the answer to 0=V+19

Answers

Answer:

v= -19

Step-by-step explanation:

Solve for  V  by simplifying both sides of the equation, then isolating the variable.

Answer:

-19

Step-by-step explanation:

+19 -19 = 0

Therefore,

V = -19

Subtract 19 from both sides 0 - 19 = -19,

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3(5b+1)(5b-1)
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WILL MARK BRAINLEST
You want to estimate how many fish there are in a pond. Suppose you cature 145 fish, tag them, and throw them back into the pond. After a couple of days, you go back to the pond and capture 580 fish, of which 29 are tagged.

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

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9/2 / 1/4

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Step-by-step explanation:

Lupita y Andrés quieren comprar un bicicleta que ven todos los días en el aparador de la tienda la cual cuesta $3 686 ( IVA incluido 16%) y tiene el 20% de descuento ¿Cuanto pagara por la bicicleta?

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your answer will be A.85°

Step-by-step explanation:

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have a great day!!!

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0,012

Step-by-step explanation:

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Hope this helps; have a great day!


Rectangles always have congruent diagonals.
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False because there is no diagonal part in the rectangle

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Answers

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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bcuz

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Answer:

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Step-by-step explanation:

3 quarters+3 nickel+1 penny=91 cents

Answer:

91 cents

Step-by-step explanation:

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Answer:

45.3 miles/h

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Step-by-step explanation:

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