A survey was conducted that asked 1003 people how many books they had read in the past year. Results indicated that x overbar equals 12.8 books and sequels 16.6 books. Construct a 99% confidence interval for the mean number of books people read. Interpret the interval.

Answers

Answer 1

Answer:

Answer:

The 99% confidence interval would be given (11.448;14.152).

Step-by-step explanation:

1) Important concepts and notation

A confidence interval for a mean "gives us a range of plausible values for the population mean. If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean"

$s=16.6$ represent the sample deviation

$\bar X=12.8$ represent the sample mean

n =1003 is the sample size selected

Confidence =99% or 0.99

$\alpha=1-0.99=0.01$ represent the significance level.

2) Solution to the problem

The confidence interval for the mean would be given by this formula

$\bar X \pm z_(\alpha/2) (s)/(√(n))$

We can use a z quantile instead of t since the sample size is large enough.

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=2.58$

And replacing into the confidence interval formula we got:

$12.8 - 2.58 (16.6)/(√(1003))=11.448$

$12.8 + 2.58 (16.6)/(√(1003)) =14.152$

And the 99% confidence interval would be given (11.448;14.152).

We are confident that about 11 to 14 are the number of books that the people had read on the last year on average, at 1% of significance.

Related Questions

Sean bought a laptop and a printer. He sold both items for £1,500 getting £1,350 just for the laptop. Sean made a 24% profit on the cost of the printer. What was the cost of the printer? Give your answer to 2 decimal places.
What is 2.5 % of 16 ?
Ngozi earns \$24{,}000$24,000dollar sign, 24, comma, 000 in salary in the first year she works as an interpreter. Each year, she earns a 3.5\%3.5%3, point, 5, percent raise. Write a function that gives Ngozi's salary S(t)S(t)S, (, t, ), in dollars, ttt years after she starts to work as an interpreter.
Please help!!!!!!!!!!!
Christine has $875.83 In her savings account the account pays 9% compounded monthly. Christine does not make any deposits or withdrawals over the next six months how much interest does the account earn

If the radius of a circle is increased by 100%, then the area is increased by:(A)100% (B) 200% (C) 300% (D) 400% (E) none of these

Answers

$A_1=\pi r^2\n\nR=2r\ then\ A_2=\pi R^2\to A_2=\pi(2r)^2=4\pi r^2\n\nA_2-A_1=4\pi r^2-\pi r^2=3\pi r^2=3A_1\n\n3=300\%\n\nAnswer:(C).$

hope this helps in the picture below :)

What is the slope of the line 4x + 6y = 12

Answers

I believe its going to be (3,2) because you take 12 and divide it by 4 which gives you your x value of 3 then you take 12 and divide it by 6 which gives you your y value of 2

4x+6y=12
-4x -4x
6y=-4x+12
-6 -6

Answer: Y= -4x+12

Each student wrote a two step equation. peter wrote the equation 4x - 2 =10, and andres wrote the equation 16x - 8 = 40. the teacher looked at their equations and asked them to compare them. describe one way in which the equations are similar

Answers

4x-2=10
answer is 3
16x-8=40
answer is 2
they are all even numbers. it is all divisible.by 4
I think

Jeremy got a haircut and paid 15% as a tip.A. what percent of the cost did jeremy pay the barber, including the tip:

B. what is the cost of the haircut

C. calculate the total cost of the haircut, including the tip

D.If you only wanted to know the tip amount, how would you change the process you used in part c to calculate the total cost

Answers

Answer:

Sure! Here are the answers:

A. Jeremy paid 100% + 15% = **115%** of the cost to the barber, including the tip.

B. Let's say the cost of the haircut is x dollars. Then, Jeremy paid a tip of 15% of x which is 0.15x dollars. Therefore, the cost of the haircut is x + 0.15x = **1.15x** dollars.

C. The total cost of the haircut, including the tip is 115% of the cost of the haircut. So, if the cost of the haircut is x dollars, then the total cost is 115% of x which is 1.15x dollars.

D. If you only wanted to know the tip amount, you would calculate 15% of the cost of the haircut which is 0.15 times x or **0.15x** dollars.

I hope this helps!

Step-by-step explanation:

Which relation is a function? help me
A.
{(7, 12), (1, –5), (3, –10), (2, –5)}

B.
{(1, 2), (1, 5), (1, –1), (1, 4)}

C.
{(–3, 4), (–2, 5), (0, 9), (0, 12)}

D.
{(8, –1), (2, –1), (3, 8), (2, 5}

Answers

Function is a relation where each x-coordinate pair with only one y-coordinate.

A is the only option where x-coordinates do not repeat. So A is the answer.

Caroline bought 20 shares of stock at 101/2, and after 10 months the value of the stocks was 111/4. If Caroline were to sell all her shares of this stock, how much profit would she make? A. $15 B. $10 C. $225 D. $210