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.)

Answer:

Step-by-step explanation:

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:

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:

[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

X increased by 10 is equal to 42

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)

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

Q8 Change 12 g to kilograms,​

2/5 of 16= (estimate each product)

What is the value of n?

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

Which function is best represented by this graph?

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?

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

Will give brainly Simplify 5/10

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. ​

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

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

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

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

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

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

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?

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

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.

Need help asap
Question 6

Rectangles always have congruent diagonals.
False
True
False

What is the answer to 0=V+19

Please help 30 points pls

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

Zander found these coins in his Couch

What is 1+1 I need help

40 points! Please help me

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