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

2[tex]\sqrt{64[/tex]

Answers

the answer is 0.03125

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?

Answers

Haoeiwhah63618463642

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

Justin is going to invest $31,000 and leave it in an account for 7 years.
Assuming the interest is compounded quarterly, what interest rate, to the
nearest tenth of a percent, would be required in order for Justin to end up
with $45,000?

Answers

Answer:

5.4 percent

Step-by-step explanation:

Need help asap
Question 6

Answers

Answer:

AC=30

BD=30

BE=15

AB=27

Answer:

AC = 30, BD = 30, BE = 15, AB = 27, BC = 13.1

Step-by-step explanation:

AC = AE * 2

BD = BE * 2

BE = AE

AB = CD

BC = [tex]\sqrt{30^{2}-27^{2} }[/tex] (Pythagorean theorem)

3) 75b^2-3 what is this factored please

Answers

3(5b+1)(5b-1)
hope it helps

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

13y = 182

y = 14

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

y=14

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,

-19 = V


Rectangles always have congruent diagonals.
False
True
False

Answers

False because there is no diagonal part in the rectangle

X increased by 10 is equal to 42

Answers

Answer:

x = 32

Step-by-step explanation:

x + 10 = 42, then you subtract 10 from both sides to get 32

The answer is treh I hunk

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

    = 4.75 × b

38 = 4.75b

b = 38 ÷ 4.75

b = 8

Answer:

4.75 & 8

Step-by-step explanation:

Hope this helps

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 :

i) mean = 20.36

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 )

where n = sample size

hence position of median value = 11 + 1 / 2 = 12 / 2 = 6

the value at the 6th position = 21 ( median )

iii) mode

mode = most repeated value in the series of data

hence mode value = 21

Zander found these coins in his Couch

Answers

Answer:

91 cents

Step-by-step explanation:

3 quarters+3 nickel+1 penny=91 cents

Answer:

91 cents

Step-by-step explanation:

3 quarters=75c

3 nickels=15c

1 penny=1c

75c+15c+1c=91 cents

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.

An estimate for the number of fish in the pond is
fish

Answers

Answer:

450fish estimate

Step-by-step explanation:

Each triangle in the net below has a base of 6 centimeters and a height of 8 centimeters. What is the surface area, in square centimeters, of the figure represented by the net? helpppppp i need help pls

Answers

The area of a triangle is 1/2 x base x height.

The area of the triangle is 1/2 x 6 x 8 = 24 square cm.

There are 4 identical triangles so 24 x 4 = 96 square cm.

The area of the square base = 6 x 6 = 36 square cm.

Total area = 96 + 36 = 132 square cm.

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. ​

Answers

Answer:

34

24

Step-by-step explanation:

divide 25 by 3

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

C=(-7)^2-4x1x13

D=-3

2 imaginary numbers

Will give brainly Simplify 5/10

Answers

1/2 , 5 is half of 10 and if you divide each number by 5 you get 1/2

A car travels 30 – miles in
304
of an hour. What is the average speed, in miles per hour,
of the car?​

Answers

Answer:

45.3 miles/h

Hope this will help you

Step-by-step explanation:

45.3h miles

welcome







20 letters

The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.​

Answers

Answer:

24.5

Step-by-step explanation:

Determine whether the sequence converges or diverges. If it converges, find the limit. [Hint:
consider limit laws, the Squeeze Theorem, behavior of related real-valued functions, etc.]
(a) an = 2 + (0.86)^n
(b) an =(4^n)/(1+9^n)
(c) an = arctan(ln n)

Answers

(a) converges; consider the function f(x) = a ˣ, which converges to 0 as x gets large for |a | < 1. Then the limit is 2.

(b) converges; we have

4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)

As n gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.

(c) converges; we know ln(n ) → ∞ and arctan(n ) → π/2 as n → ∞. So the limit is π/2.

Q8 Change 12 g to kilograms,​

Answers

Answer:

0,012

Step-by-step explanation:

12 grams is 0.012 kilograms.

Hope this helps; have a great day!

What is the value of n?

Answers

Answer:

your answer will be A.85°

Step-by-step explanation:

hope it helps you

have a great day!!!

What is the approximate area of the shaded region in the given square containing 2 semicircles? (Use * 3.14.) 10 cm 0 21.5 square centimeters O 50 square centimeters O 78.5 square centimeters O 100 square centimeters

Answers

Answer:

yes

Step-by-step explanation:

bcuz

Answer:

Subtract the circle from the square

Step-by-step explanation:

(10× 10) - 25pi

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.

Determine the missing number in the equation 3+7=+4 ANSWER QUICKLY PLEASE

Answers

Answer:

-6

Step-by-step explanation:

3+7=10

10-6=4

so 3+7-6=+4

hope this helps

Answer:

6

Step-by-step explanation:

= means the same as

3+7 = 10

therefore 4 + ?=10

10-4=6

therefore the missing number is 6

=6

Divide. Write your answer in simplest form. 9/2 / 1/4

Answers

Answer:

18

Step-by-step explanation:

9/2 / 1/4

keep 9/2

Change the operation to multiplication

flip 1/4 into 4 or 4/1

multiply on top and bottom and get 36/2

which 36/2 is 18 and 18 is the answer

Brainliest?

It has to be 18 use Socratic

In AQRS, the measure of _S=90°, SQ = 13 feet, and QR = 59 feet. Find the measure
of ZR to the nearest tenth of a degree.

Answers

Answer:

Step-by-step explanation:

12.7

What is 1+1 I need help

Answers

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?

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the -2 in the answer is the y intercept. 1/4 is the slop. rise over run, so up one and over four

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