What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D

Answers

Answer 1

Answer:

The expression for the required minimum sample size is \(n=[\frac{1.645\times\sigma }{D}]^{2}\).

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

 \(CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

The margin of error for this interval is:

 \(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

Confidence level = 90%

α = 10%

Compute the critical value of z for α = 10% as follows:

 z = 1.645

*Use a z-table.

Compute the sample size required as follows:

 \(MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

\(n=[\frac{z_{\alpha/2}\times\sigma }{MOE}]^{2}\)

\(n=[\frac{1.645\times\sigma }{D}]^{2}\)

Thus, the expression for the required minimum sample size is \(n=[\frac{1.645\times\sigma }{D}]^{2}\).


Related Questions

Juan determines that a triangle has sides that measure 5 cm, 12 cm, and 13 cm. The same triangle also has one 90°° angle and two angles that are less than 90°°. Which best describes the triangle Juan is measuring?
isosceles right

scalene acute

scalene right

equilateral right

Answers

Answer:

scalene right

Step-by-step explanation:

A scalene right has no equal side lengths, has a right side(90) and will have two angles less than 90 because all three triangle sides need to equal to be 180. So scalene right is your answer. Hope that helped!

Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%. Select all the true statements. The proportion that represents the down payment is 20100=125,000 20 100 = 125 , 000 x . The down payment is $25,000. The proportion that represents the down payment is 20100=125,000 20 100 = x 125 , 000 . The down payment is $50,000. The down payment is 15 1 5 of the cost of the house.

Answers

The correct options are -

The proportion that represents the down payment is : 20/100 x 125000.The down payment is $25,000

What is down payment?

When something is bought on credit, an initial payment is made in the form of a down payment.

Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.

We can calculate the amount she is putting in down payment as -

{x} = 20% of 125000

{x} = 20/100 x 125000

{x} = 20 x 1250

{x} = 25000

Therefore, the correct options are -

The proportion that represents the down payment is : 20/100 x 125000.The down payment is $25,000

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{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above:
DONE
Domain
-3
4
-1
5
Range
3
7
-2
The mapping diagram above:
DONE
y=x²
DONE
x
-3
-1
y
5
2
-1
The table above:
DONE ✔

{ (-2, 4), (0, 2), (-1, 3), (4, -2)}The set of ordered pairs above:DONEDomain-34-15Range37-2The mapping

Answers

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

What is a function?

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Find the component form and magnitude of the vector v with the given initial and terminal points. Then find a unit vector in the direction of v.
Initial point:
(1, 6, 0)
Terminal point:
(4, 1, 6)

Answers

The component form of the vector is <3, -5, 6>, the magnitude of the vector is √70, then the unit vector is <0.386, -0.643, 0.643>.

The initial and terminal points to find the component form of the vector, calculated its magnitude, and then divided the component form by the magnitude to find a unit vector in the direction of v.

To find the component form of the vector, you can subtract the coordinates of the initial point from the coordinates of the terminal point. In this case, we have:

v = (4, 1, 6) - (1, 6, 0)

v = (3, -5, 6)

So the component form of the vector is v = <3, -5, 6>.

To find the magnitude of the vector, we can use the formula:

|v| = √(3² + (-5)² + 6²)

|v| = √70

Therefore, the magnitude of the vector is √70.

Finally, to find a unit vector in the direction of v, we can divide the component form of v by its magnitude:

u = v/|v|

u = <3/√70, -5/√70, 6/√70>

So the unit vector in the direction of v is u = <0.386, -0.643, 0.643>.

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Find the value of x
X + 90
100°

Find the value of xX + 90100

Answers

10 is the answer sorry don’t know how to explain jus trust me

Find the values of m and b

Find the values of m and b

Answers

Value of m and b of the straight line in the graph is 0 and 2 respectively.

Define slope

In mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.

Let us assume that the equation of line be y=mx+b.

where m is the slope

and b is the intercept

The line in the graph is parallel to x axis

so, slope is 0

m=0

the line passes through(0,2)

Putting the value in the equation, we get

b=2

Hence, the equation of line be y=2

Therefore, value of m=0 and b=2.

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The complete question is:

The graph is showing the equation of straight line y=mx+b, find the value of m and b.

Image is attached below:

Find the values of m and b

How many buckets of balls does the golf course need to sell
if 10 course packages are sold?
If 10 course packages are sold, the golf course must sell
buckets of balls.
Check

Answers

爷爷,圣诞节快到了,但是我不想要任何礼物,只有你活着,呼吸和健康。那是我的圣诞愿望

what is the solution to 0.5(5x+1)=3

Answers

Let’s solve the equation
0.5(5x+1) = 3
= 2.5x + 0.5 = 3
= 2.5x = 3 - 0.5
= 2.5x = 2.5
= x = 1
Hope it helped !!!
Comments below

Answer:

1

Step-by-step explanation:

Divide each term by  

0.5  and simplify.

Divide each term in  

0.5 ( 5 x + 1 ) = 3  by  0.5 . 0.5 ( 5 x + 1 ) 0.5

= 3 0.5 Cancel the common factor of  0.5 . 5 x + 1 = 3 0.5  Divide  3  by  0.5 .

5 x  + 1  = 6

Move all terms not containing  

x

to the right side of the equation.

Subtract  1  from both sides of the equation.

5 x  =  6  −  1  Subtract  1  from  6 . 5 x =  5

Divide each term by  

5  and simplify.

Divide each term in  5 x = 5  by  5 . 5 x 5 = 5 5

Cancel the common factor of  5 .

Cancel the common factor.

5 x 5 = 5 5  Divide  x  by  1 .  x = 5 5  Divide  5  by  5 .

x  =  1

Is every relation also a function?

Answers

Answer:

No,

Every relation isn't a Function but every function is a relation.

[7] Which country is known as the ‘Land of Thunderbolts’?
(A) China

(B) Bhutan

(C) Mongolia

(D) Thailand












































IAS CHINADU KUMAR KHAN

Answers

Answer: CHINA

Step-by-step explanation:

IAS CHINADU

Answer:

Bhutan is the answer.

Find the missing side. 31° Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21​

Find the missing side. 31 Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21

Answers

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

find the slope of any parallel to the line passing through G (2, -3) and H ( -1, 4)

Answers

Answer:

\(-\frac{7}{3}\)  or -2.333333333

Step-by-step explanation:

 to fine the slope you use rise/run= \(\frac{(-3)-4}{2-(-1)}\)  

What value of x makes the equation true?
1.42 +2.6x = -16

Ox= -4
Ox= -13
Ox= -19
Ox = -48

Answers

I am pretty sure I would have to be -4

find a solution y = 3 x − 4

Answers

Answer: The equation y = 3x - 4 is a linear equation in slope-intercept form, where the slope (3) is the coefficient of x and the y-intercept (-4) is the constant term. To find a solution for this equation, we can substitute a specific value of x and solve for the corresponding value of y.

For example, if we let x = 2, we can substitute it into the equation:

y = 3(2) - 4 = 6

So the solution for x=2 is y=6

We can also graph this equation, it will be a straight line with slope 3 and y-intercept (-4)

Step-by-step explanation:

Any help would be appreciated!

Any help would be appreciated!

Answers

Answer:

this might help you....

Any help would be appreciated!
Any help would be appreciated!

Answer:

See below.

Step-by-step explanation:

In the figure above, ∠WXY and ∠YXZ are a linear pair.

What is a Linear Pair?

A Linear Pair is 2 angles that are adjacent, and form a straight line when combined. A Linear Pair contains 2 Supplementary Angles, angles that add up to 180°.

Their measures add up to 180°.

In order to find y, because they're a linear pair, we can set up an equation with the 2 angles equal to 180°.

\(4y+6y+30=180\)

Combine Like Terms:

\(10y+30=180\)

Subtract 30 from Both Sides:

\(10y=150\)

Divide by 10:

\(\frac{10y}{10} = \frac{150}{10} \\y = 15.\)

The value of y is 15.

Now since we know the value of y, we can substitute 15 into each angle to find their measure.

Substitute:

\(4(15)=60\\6(15)+30=120\)

The measure of ∠WXY is 60° and the measure of ∠YXZ is 120°.

Find the perimeter of the parallelogram shown below

Find the perimeter of the parallelogram shown below

Answers

it’s 197 good luck!!!

As per the dimension of the parallelogram, the perimeter of the parallelogram is 192 units.

Identify the sides: The given values represent the lengths of three sides of the parallelogram. Side a and side b are the base and the opposite side, respectively. The height (h) is the perpendicular distance between the base (a) and the opposite side (b).

Perimeter formula: The perimeter (P) of a parallelogram is the sum of the lengths of all four sides. Since opposite sides of a parallelogram are equal in length, the perimeter formula can be expressed as

P = 2(a + b).

Calculate the perimeter: Now, we will substitute the given values into the perimeter formula to find the perimeter of the parallelogram:

P = 2(a + b)

P = 2(49 + 47)

P = 2(96)

P = 192

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Need help will give brainliest and a good rating!

Need help will give brainliest and a good rating!

Answers

Answer:

1) x = -6, 8

2) x = -1 + i√2

Step-by-step explanation:

1)

\( {x}^{2} - 2x - 48 = 0\)

\((x - 8)(x + 6) = 0\)

x = -6, 8

2)

\(3 {x}^{2} + 2x + 1 = 0\)

x = (-2 + √(2^2 - 4(3)(1))) / (2 × 1)

x = (-2 + √(4-12)) / 2

x = (-2 + √-8) / 2

x = (-2 + 2i√2) / 2

x = -1 + i√2

What is the slope of the following line?

What is the slope of the following line?

Answers

Answer:c, the answer is c

Step-by-step explanation:

The Perimeter of a triangle is 90 cm. The triangle has side lengths of 2x + 5, 4x - 10, and x + 4. Find the value of x and the length of each side.

Answers

Answer:

I don't understand oof oof

Step-by-step explanation:

Can y’all help me on question 6?!

Can yall help me on question 6?!

Answers

Answer:

B is the answer- positive y and negative x

f(x)=-12x^3-14x^2+6x

Answers

There has to be x equals of f is something or u can’t solve

Blake is saving up to buy a
new pair of headphones. He
has $20 saved already, and
he earns $ 10 for every lawn
he mows. How many lawns will
he have to mow to have at
least $90 saved?

Answers

Answer: He will need to mow 7 lawns.

Step-by-step explanation:

He already has $20

90-20=70

70/10=7

You are considering two job offers. The first job pays $15.75 per hour. The second job pays $12.00 per hour plus $1.25 per unit produced per hour. How many units must you produce per hour for the second job to pay more per hour than the first job?

Answers

Answer:

4 more units

Step-by-step explanation:

1.25x + 12.00 > 15.75

1.25(4) =5

5 + 12 = 17

Which letter has rotational symmetry?

V
E
M
X

Answers

Step-by-step explanation:

Letter X has rotational symmetry

Write an equation for the description.

Hector is visiting a cousin who lives 300 miles away. He has driven 95 miles. How many more miles does
he need to drive to reach his cousin's home? Let d be how many miles left to reach his cousin's home.

Answers

d=300-95
d=205
Hector has 205 more miles to go

Type the correct answer in each box. Use numerals instead of words.
Consider function h.

Type the correct answer in each box. Use numerals instead of words.Consider function h.

Answers

The correct value for the given equation h(x) is h(0) = 10 and h(4) = 16.

What is Signum Function?

The sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

Here,

h(0) = 2 X 0² - 3 X 0 + 10 = 10

and h(4) = 2⁴

      h(4) = 16

Thus, the correct value for the given equation h(x) is h(0) = 10 and h(4) = 16.

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Leah is training for a bike race. She starts by biking 8 miles during every training session,
Each week she plans to increase the distance of her training session by mile
3/4 miles.

Let w be the number of weeks. Write an expression to show the distance Leah
bikes in a training session after w weeks

Leah is training for a bike race. She starts by biking 8 miles during every training session,Each week

Answers

Answer:

3/4 W + 8 = M. M is the total miles

The required expression to show the distance Leah bikes in a training session after w weeks is 8 + 3w/4.

Given that,
She starts by biking 8 miles during every training session, and each week she plans to increase the distance of her training session by 3/4 miles.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

She starts by biking 8 miles during every training session,
increase the distance of her training session by mile 3/4 miles
Let w be the number of weeks.
Total increase = 3w / 4
Total distance travel = 8 + 3w/4

Thus, the required expression to show the distance Leah bikes in a training session after w weeks is 8 + 3w/4.

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In Monopoly one rolls a pair of dice. Find the probability of getting a sum of 12. Round your answer to 3 digits after the decimal point.

Answers

Answer:

the probability of rolling a sum of 12 on a pair of dice in Monopoly is approximately 0.028.

Step-by-step explanation:

There are 6 possible outcomes on each die, so there are 6 x 6 = 36 possible outcomes when rolling a pair of dice. To find the probability of getting a sum of 12, we need to count the number of outcomes that add up to 12 and divide by the total number of outcomes.

The only way to get a sum of 12 is to roll a 6 on both dice. There is only 1 way to do this, so the number of outcomes that add up to 12 is 1.

Therefore, the probability of getting a sum of 12 is:

1/36 ≈ 0.028 (rounded to 3 decimal places)

So the probability of rolling a sum of 12 on a pair of dice in Monopoly is approximately 0.028.

Which is true about the polynomial ?It is a binomial with a degree of 2.It is a binomial with a degree of 3.It is a trinomial with a degree of 2.It is a trinomial with a degree of 3.Polinomial: 9x^2y-6x-5y^2

Answers

Explanation

We must classify the following polynomial:

\(9x^2y-6x-5y^2.\)

Looking at this polynomial, we see that:

• it has three terms ⇒ it is a trinomial,

,

• the term with the highest degree is 9x²y with degree 2 + 1 = 3 ⇒ the polynomial has degree 3.

We conclude that we have a trinomial with a degree of 3.

Answer

It is a trinomial with a degree of 3.

Find the equation of a straight line cutting off the y-intercept 4 from the axis of y and inclined to 60° with the positive direction of X-axis.

Answers

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

How to define a linear function?

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

m is the slope.b is the intercept.

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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