The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.23.

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 98% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Answers

Answer 1

Using the z-distribution, it is found that a sample size of 1066 is 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 z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which z is the z-score that has a p-value of .

The margin of error is:

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

From the previous study, the estimate is of 0.23, hence [tex]\pi = 0.23[/tex].

98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so [tex]z = 2.327[/tex].

The sample size is n for which M = 0.03, hence:

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

[tex]0.03 = 2.327\sqrt{\frac{0.23(0.77)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.327\sqrt{0.23(0.77)}[/tex]

[tex]\sqrt{n} = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)^2[/tex]

[tex]n = 1065.5[/tex]

Rounding up, a sample size of 1066 is required.

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Related Questions

Q5). If A={3,4} B= {2,3,4} C={3,4,5} then find (BxB) ∩ (CxC)​

Answers

Step-by-step explanation:

Given that

A = {3,4}

B = { 2,3,4}

C ={3,4,5}

BXB = {2,3,4}×{2,3,4}

⇛ {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4),(4,2),(4,3),(4,4)}

and

CXC = {3,4,5}X{3,4,5}

⇛ {(3,,3),(3,4,)(3,5),(4,3),(4,4),(4,5),(5,3),(5,4),(5,5)}

Now

(BxB) n(CxC)

⇛ {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4),(4,2),(4,3),(4,4)} n

{(3,,3),(3,4,)(3,5),(4,3),(4,4),(4,5),(5,3),(5,4),(5,5)}

⇛ {(3,3),(3,4),(4,3),(4,4,)}

Additional comment:

AxB is the Cartesian product of the two sets A and B on which (a,b) form a belongs to A and b belongs to B

AnB is the set of Common elements in both A and B

Help help help help help pleases pelass thank you

Answers

Answer:

a' (-6,7) b' (-5,3) c'(-2,4)

Step-by-step explanation:

PLEASE HELP>>>>>
25 POINTS...................

Answers

Answer:

y = 2/3x - 9

Step-by-step explanation:

note the slope, then note the y intecept, then plug it into the equation y = mx+b

Answer:

So its d

Step-by-step explanation:

Y intercept is 6, and the slope is 3/2. hope i help! And if it isn't that, its c

two improper fractions between 4 and 5

Answers

Answer:

[tex] \frac{9}{2} [/tex]

[tex] \frac{13}{3} [/tex]

helppppppppp
what is -12x<60

Answers

Answer:

x > -5

Step-by-step explanation:

-12x < 60

To solve the equation for x, we want x to be by itself on one side.  Let's start by dividing both sides by -12:

-12x/-12 < 60/-12

When dividing or multiplying by a negative number, we have to turn around the inequality sign, so now we have:

x > 60/-12

And 60/-12 = -5, so:

x > -5

brief statement Bosnian Crisis.

Answers

Answer:

The Bosnian war and genocide resulted in close to 100,000 civilians killed, over 2 million people forcibly displaced, and between 20,000-50,000 women systematically raped. ... Over 7,000 Bosnian Muslim prisoners captured in the area around Srebrenica were summarily executed from 13 July to 19 July 1995.

Step-by-step explanation:

hope this helps

Plot the image of quadrilateral ABCD under a reflection across line L

Answers

                          hope this helps                                    

Step-by-step explanation:

The coordinates of the reflection of a point (x, y), across the y-axis is the point (-x, y)

Please find attached the plot of the image of quadrilateral ABCD under a reflection of the line l

Method:

The coordinates of the vertices of the given quadrilateral ABCD are as follows

A(-2 0), B(-3, 4), C(0, 4), and D(-1, 1)

Due to its orientation, the line l can be taken as being equivalent to the y-axis

The coordinates of the image of (x, y) following a reflection across the y-axis is (-x, y)

Therefore, for the image of the quadrilateral ABCD following a reflection across the y-axis to give the quadrilateral A'B'C'D', the coordinates of A'B'C'D' are;

A(-2 0), reflected across the y-axis gives the image A'(2, 0)

B(-3, 4), reflected across the y-axis gives the image B'(3, 4)

C(0, 4), reflected across the y-axis gives the image C'(0, 4)

D(-1, 1), reflected across the y-axis gives the image D'(1, 1)

The coordinates with which the image of the of the quadrilateral ABCD can be plotted are therefore;

A'(2, 0), B'(3, 4), C'(0, 4), and D'(-1, 1)

The plot of the quadrilateral ABCD and the image A'B'C'D' can be created using MS Excel presented in the attached graph

Learn more about transformations here:

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laminiaduo7 and 1 more users found this answer helpful

1.1 is the result of finding the product of 1/2 and 3 minus a number. What is the number?
A. 5 1/5
B. 2 9/20
C. 4/5
D. -19/20

Answers

Answer: i think the answer is B.

Step-by-step explanation:

D can’t be correct cause it’s a negative and there’s no negatives in the question , if you look at B 2 9/20 can go into 1/2.

Answer:

C. 4/5

Step-by-step explanation:

k12

Patrick is paid
$12 for 3 hours of work
How many hours does she work is she gets payed $1

Answers

Answer:

Step-by-step explanation:

Answer:

0.25 Hours or 15 minutes

Step-by-step explanation:

Please give me brainliest

Lauren spends her allowance $50 a month on make up and CDs. She spends $10 more a month on CDs than she does on make up. How much money does she spend every month on each product

Answers

Answer:

$30 on CDs

$20 on Makeup

hope it helps

Step-by-step explanation:

The money spent on each product is $20 and $30 respectively.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Given that,

The money spent by Lauren on make up and CDs is $50.

Suppose the money spent on CDs be x.

Then, the money spent on make up is  x + 10.

As per the question the following equation can be formed,

x + x + 10 = 50

=> 2x + 10 = 50

=> 2x = 40

=> x = 20

Thus, money spent on make up is 20 + 10 = 30 dollars.

Hence, the money spent on CDs and make up is $20 and $30 respectively.

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The ratio of boys to girls in the class is 4 to 5. If there are 18 boys and girls in the
class, how many of each are there?

Answers

Answer:

8 boys and 10 girls

Step-by-step explanation:

If the ratio is 4:5,

4x2 + 5x2 equal 8+10 =

18.

4:5=8:10

Answer:

8 boys

10 girls

Step-by-step explanation:

4:5

8:10

8+10=18

-2x + 8 > 22
im a little stuck help

Answers

Answer:

Step-by-step explanation: am sorry but I don’t know nothing

What is the coefficient in this expression?

3/4mn

4

n

34

3

Answers

Since it is the term that multiplies the variables, the coefficient is of [tex]\frac{3}{4}[/tex].

In an algebraic expression, the coefficient is the term that multiplies the variables.

In this problem, the expression is:

[tex]\frac{3}{4}mn[/tex]

The variables are m and n.They are multiplied by [tex]\frac{3}{4}[/tex]

Hence, the coefficient is of [tex]\frac{3}{4}[/tex].

A similar problem is given at https://brainly.com/question/24417465

What is 5m + 5n where m = 10 and n = -5?

A. 25
B. 26
C. 62
D. 52

ADD EXPLANATION IF NECESSARY. TYSM! :D​

Answers

Answer:

A

Step-by-step explanation:

5 times 10= 50

5 times -5= -25

50-25=25

What fraction of the rectangle is shaded? PLS PLS PLS help ASAP! Ty

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Calculate the total area of the rectangle:

21 x 12 = 252

Half of the rectangle is unshaded so:

252 ÷ 2 = 126

For clarification, side A is the top, side B is the left hand side and side C is the bottom.

Now, find the area of the unshaded side of the other triangle. As the length of side C is 21 and the shape is a rectangle, side A is also 21. We need to calculate the amount is unshaded on this side so:

21 - 14 = 7

(7 x 12) ÷ 2 = unshaded

84 ÷ 2 = 42

So now we know the total of the shape that is shaded, we can now subtract this from the total area of the shape:

252 - 126- 42 =   84

Which in fraction form is:

[tex]\frac{84}{252}[/tex]

This can be simplified down by dividing both the numerator and the denominator by 3:

[tex]\frac{84 \div 3}{252 \div 3}[/tex]

=[tex]\frac{1}{3}[/tex]

Hope this helps!

Kelly watches 3/5 of a movie in 5/8 of an hour. How much time wil it take her to watch the entire movie?

Answers

well, putting the movie in fifths, she watched 3/5, the whole movie will be 5/5 = 1.

[tex]\begin{array}{ccll} \stackrel{movie}{fraction}&hour\\ \cline{1-2} \frac{3}{5}&\frac{5}{8}\\[1em] \underset{whole}{1}&x \end{array}\implies \cfrac{~~ \frac{3}{5}~~}{1}=\cfrac{~~ \frac{5}{8}~~}{x}\implies \cfrac{3}{5}x=\cfrac{5}{8}\implies \cfrac{3x}{5}=\cfrac{5}{8} \\\\\\ 24x=25\implies x = \cfrac{25}{24}\implies x = 1\frac{1}{24}\qquad \textit{1 hour, 2 minutes and 30 seconds}[/tex]

Find total cost to the nearest cent.$1500 computer; 7% tax

Answers

Answer:

Total Cost = $1605

Step-by-step explanation:

Total Cost = Cost of the Computer +  (Cost of the computer × tax %)

Total Cost = $1500 + ($1500 × .07)

Total Cost $1500 + $105

Total Cost = $1605

HELP ME OUT PLEASE

Which equation could represent the relationship shown in the scatter plot?

A) y = -3x - 2

B) y = 9x -1/2

C) y = -3/4x + 10

D) y = -2/3x + 1​

Answers

Answer:

C) y = -3/4x + 10

Step-by-step explanation:

Slope is negative and its value (-3/4) can be determined from the line.

The line crosses the axis of ordinates at y = 10, when x = 0. If you substitute x for 0 in y = -3/4x + 10, y = 10. This corresponds to the line drawn in scatter plot.

Anne and chima are to share a sum of money in ratio 4:1.Anne obtains #6000.what is chima's share?​

Answers

Answer:

Chima would obtain 1200

I really need help. Can someone help me with making a linear, quadratic and exponential models. All models need to include the regression line, regression equation and the coefficient of determination.

Answers

y=2500x^1+ i d k i can't see the y-intercept

Divide $5100 in the ratio 4:3

Answers

Answer:$2914.26:$2185.71


f(x) = 3x + 1 and f-1 = f-1 = x-1 / 3
then f -'(7) =

Answers

Answer:

2

Step-by-step explanation:

f^-1 (7) = [tex]\frac{x-1}{3}[/tex] = [tex]\frac{7-1}{3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

Extra Points and Brainliest Award if answered!!!!
Gerald is testing to see if a possible rational root is an actual rational root of a polynomial. He uses synthetic division to determine the value of the remainder.
Which theorem is he using to test the value?

A. Linear Factorization Theorem

B. The Fundamental Theorem of Algebra

C. The Factor Theorem

D. The Remainder Theorem

Answers

Answer:

its C.

Step-by-step explanation:

please mark me brainlists

Gerald used the factor theorem to test the value. Therefore, option C is the correct answer.

Given that, Gerald is testing to see if a possible rational root is an actual rational root of a polynomial.

What is Synthetic Division?

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.

The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0. In other words, we can say that (x - a) is a factor of f(x) if f(a) = 0.

Therefore, option C is the correct answer.

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Ben left town a at 22:25 and arrived at Stone b at 2:40 the next morning how long did is Journey take​

Answers

Answer: The journey took 4 hours and 15 minutes.

PLEASE ANSWER!!! HELPPPO

Answers

Answer:

a) 34

b) 17

c)46

Step-by-step explanation:

55-21 = 34

count

Please take a look at the picture

Answers

Answer:

A and B

Step-by-step explanation:

They both have the same numbers and at least one of the given numbers is negative.

Hope this helps :)

I need help with the question

Answers

Answer:

[tex]A = 25\pi[/tex]  or  25 × 3.14 = 78.5m

Step-by-step explanation:

The radius is half of the diameter. So the radius = 5m  (10/2)

[tex]A = \pi r^{2}[/tex]

[tex]A = \pi (5^{2} )[/tex]

[tex]A = 25\pi[/tex]

Based on the diagram, which is a true statement?
o If a student plays in the band, then he/she is an
honor student.
Olfa student is an honor student, then he/she plays in
the band.
O If a student is not an honor student, then he/she
cannot play in the band.
O If a student is an honor student, then he/she may
also be a band member.

Answers

Answer:

top god's menu back door distract 9 call scars double knot thunderous gone away gone day SKZ ALL AROUND THE WORLD

Answer:

Step-by-step explanation:

if a student is an honor student, he/she may also be a band member

Select the correct answer from each drop-down menu.

The graph of g(x) is shown.



The graph of h(x) = g(x + 5) has
and
.

Answers

The function h(x) has a horizontal asymptote at y=5 and the  vertical asymptote is x=-2.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, h(x)=g(x+5.

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.

Here, the horizontal asymptote is 3, and the vertical asymptote is -2

The graph of h(x) = g(x+5) had a horizontal asymptote at y=5 and the same vertical asymptote as function g(x).

Therefore, the function h(x) has a horizontal asymptote at y=5 and the  vertical asymptote is x=-2.

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Which ordered pair is a solution of the
equation?
Y= 32x+5

Answers

Step-by-step explanation:

where are the ordered pairs?

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