The probability of getting exactly 0 heads is, 0.031.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
A fair coin is tossed 5 times.
So, the the total number of possibilities are,
[tex]2^5= 32[/tex]
We have to find the probability of getting exactly 0 heads.
The only possible set of flips that yields 0 heads is {T, T, T, T, T}.
So,
The probability is, [tex]\frac{1}{32}=0.03125[/tex]
Probability ≈ 0.031
Hence, the probability of getting exactly 0 heads is, 0.031.
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Determine the range of the following graph
Answer: R: yE[-8,7]
Step-by-step explanation:
a quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions. how many questions should the student expect to answer correctly?'
According to the binomial distribution, there are 13 questions should the student expect to answer correctly.
Binomial distribution:
in statistics, binomial distribution refers the probability of getting a success must remain the same for the trials we are investigating.
Given,
A quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions.
Here we need to find how many questions should the student expect to answer correctly.
While we looking into the given question, we have identified that the total number of questions is 24.
Number of options = 4
So, the probability of getting correct answer = 1/4 = 0.25
The probability of getting incorrect answer is,
=> 1 - 1/4 = 3/4 = 0.75
So, based on the binomial distribution,
X ~ Binomial Distribution (m=25, p=0.25, q=0.75)
Then in probability it can be written as,
=> P (X=13) = (25C13)x ((0.25)¹³) x ((0.75)¹²)
=> P (X=13) = 0.00245461663
Therefore, the number of correct answers is 13.
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let x represent the full length of a certain species of newt. assume that x has a normal probability distribution with mean 110.6 inches and standard deviation 4.9 inches. you intend to measure a random sample of n
If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.
Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.
Sampling distribution of the sample mean:
using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.
The standard deviation of the population is σ = 3.1 and the sample size is n =103, people
The standard deviation σ/√n= 3.1/√103 =0.31.
As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.
x-bar ≈ N (216, 0.31)
μ_{x-bar} = 216
σ_{x-bar} =0.31
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(complete question)
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.
Some nations require their students to pass an exam before earning their primary school degrees or diplomas. A certain nation gives students an exam whose scores are normally distributed with a mean of 414141 points and a standard deviation of 999 points. Suppose we select 222 of these testers at random, and define the random variable ddd as the difference between their scores. We can assume that their scores are independent. Find the probability that their scores differ by more than 151515 points.
The required probability that their scores differ by more than 15 points is 0.99807.
As stated in the question, a specific country administers an exam to students with scores that are regularly distributed with a mean of 41 points and a standard deviation of 9 points. Assume we randomly select two of these testers and define the random variable d as the difference in their scores.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Z = x - μ / σ
Z = 15 - 41 / 9
Z = -2.88
Now,
P(x > 15) = P (z > -2.88)
= 0.99807
Thus, the needed chance is 0.99807 and their scores differ by more than 15 points.
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10+\frac{3}{4}y=
10+
4
3
y=
\,\,43
43
Um, is there a possibility that you could clean this question up a bit? It is a little scrambled and hard to make out of the equation given. Thanks!
At breakfat diner a cup of coffee cot$2. 75 and a muffin i $3. 25. What i the ale tax on the two item if the rate i 7. 5%?
The sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.
Define the term sale tax?The government levies a consumption tax known as a sales tax on the purchase of merchandise and services. At the point of purchase, a standard sales tax is imposed, collected by the shop, and paid to the government. You must also pay sales tax, which is calculated as a percentage of both the selling price of the items and services you buy.As the stated question-
A muffin was $3.25 and A cup of coffee cost $2.75 7. 5% is the rate at the breakfast eatery.Thus,
Total cost = $3.25 + $2.75
Total cost = $6.00
Sales tax = 7.5% of $6.00
Sales tax = 7.5 x 6.00 / 100
Sales tax = $0.45
Thus, the sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.
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The correct question is-
At breakfast diner a cup of coffee cost $2. 75 and a muffin s $3. 25. What is the sale tax on the two item if the rate is 7. 5%?
henry is organizing textbooks on his bookshelf. he has a spanish textbook, a math textbook, and a history textbook. how many different ways can he line the textbooks up on his bookshelf?
Answer:
6
Step-by-step explanation:
S = Spanish book
M = Math book
H = History book
These are the different ways in which he can organize the book on his bookshelf.
SMH
SHM
MSH
MHS
HSM
HMS
There are 6 ways.
On a coordinate plane, a line goes through (negative 1, 1) and (0, negative 3). a point is at (negative 4, negative 3) and (0, negative 3). what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)? y 3 = −4(x 4) y 3 = –one-fourth(x 4) y 3 = one-fourth(x 4) y 3 = 4(x 4)
The equation of the required line would be x - 4y = 8.
What is the slope-point form of the line?
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
A line goes through the point (-1, 1) and (0,-3)
so the slope of the given line would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-1}{0-(-1)}\\\\m=-4[/tex]
And we have to find the line which passes through the point (-4, -3) and the required line is perpendicular to the given line.
As we know the product of slopes of perpendicular lines is -1.
So the slope of the required line would be = 1/4
By using a slope-point form of the line, we get
[tex]y - y_1=m(x-x_1)\\\\y-(-3)=\frac{1}{4}(x-(-4))\\\\4(y+3)=x+4\\\\4y+12=x+4\\\\x-4y=8[/tex]
Hence, the equation of the required line would be x - 4y = 8.
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Answer:
C
Step-by-step explanation:
You plan to construct a brick wall measuring 14. 5 ft. In length, 5. 5 ft. High, and 0. 5 ft. In width. If a brick measures 6 in. X 4 in. X 2 in. , how many bricks will you need? (remember to round up. ) total volume (to the nearest tenth) = cubic feet. The number of bricks =.
Using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, we know that:
A brick wall's measurements are provided by:
14.5 feet in length
Size: 0.5 feet wide
5.5 feet tall
Brick dimensions are provided by:
6 inches in length
4-inch width
2 inches tall
The number of bricks must be determined:
Thus, the number of bricks is provided by:
Number of bricks = Volume of brick wall/Volume of brick
Number of bricks = 14.5 * 5.5 * 0.5 * 12 * 12 * 12/6 * 4 * 2
Number of bricks = 1435.5
Number of bricks = 1436
Therefore, using simple mathematical operations, we know that we will require 1436 bricks to construct a brick wall.
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What is the value when the y intercept of f(x) is subtracted from the y intercept of g(x)? f(x) =3x-5 g(x) is shown in the graph below:
In the general form y = mx + c, c is the y-intercept of the line. The difference of y-intercepts is -5.2.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The equation for f(x) = 3x - 5
And, the value of y-intercept of g(x) from the graph is 0.2
The y-intercept of f(x) can be obtained by comparing it with y = mx + c, where c is the y-intercept as follows,
c = -5.
Thus, the difference of their y-intercepts as per the question is given as,
-5 - 0.2 = -5.2
Hence, the difference of the y-intercepts of f(x) and g(x) is given as -5.2.
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find a set of scalar parametric equations for the line that passes through p(3, 4, 1) and q(4, -2, -1).
A set of scalar parametric equations for the line that passes through points p(3, 4, 1) and q(4, -2, -1) : x = 3 + 4t, y = 4 - 2t and z = 1 - t
In this question, we have been given two points p(3, 4, 1) and q(4, -2, -1).
We need to find a set of scalar parametric equations for the line that passes through points p and q.
We know that a set of scalar parametric equations is,
x = x0 + at, y = y0 + bt, z = z0 + ct
Let (x0, y0, z0) = (3, 4, 1)
and (a, b, c) = (4, -2, -1).
Therefore, scalar parametric equations as:
x = 3 + 4t,
y = 4 - 2t
and z = 1 - t
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Identify the slope of the function. Interpret its meaning in terms of the problem situation.
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students; experimental and control students are matched on iq. group of answer choices within-subjects anova independent samples t test related samples t test between-subjects anova
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students within-subjects anova.
What is an ANOVA with within-subjects?
When there are identical participants in each group, a one-way repeated measures ANOVA, sometimes referred to as a within-subjects ANOVA, is used to assess whether three or more group means are different. The groups are sometimes referred to as "related" groups as a result.ANOVA within-subjects. Comparisons of the same individuals under various circumstances are included in within-subjects variables. For instance, each child's performance in the "ADHD Treatment" research was assessed four times, once after taking each of the four treatment doses for a week.A repeated measures ANOVA is another name for a within-subjects ANOVA. This kind of test is not just confined to two time periods; it is widely utilised when utilizing a pretest and posttest design.To know more about anova check the below link:
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on january 1 electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31. they are issued at $680,186 and their market rate is 10% at the issue date. after recording the entry for the issuance of the bonds, bonds payable had a balance of $740,000 and discount on bonds payable had a balance of $59,814. electro uses the effective interest bond amortization method. the first semiannual interest payment was made on june 30. complete the necessary journal entry for the interest payment date of june 30 by selecting the account names from the drop-down menus and entering the dollar amounts in the debit or credit columns.
The interest payments is $27,750 and the Bond payable discount is $6,259
The electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31.
They are issued at $680,186 and their market rate is 10% at the issue date
Interest payments = $740,000 x 7.5% x 1/2 = $27,750 (the credit to Cash).
bond interest expense = carrying value at 1/1/13 (the beginning of the period) of $680,186 x market rate of 10% x 1/2 = $34,009 (the debit to Bond interest expense).
Bond payable discount
The discount amortization $34,009 - $27,750 = $6,259
Therefore, the interest payments is $27,750 and the Bond payable discount is $6,259
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Find x: 2x=1
X=1/2
X=1
X=2
X=-1
Answer: x = 1/2
Step-by-step explanation:
2(1/2)=1
1=1
The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "56 of a number is 30."
What is the solution set of the equation?
Responses
{10}
open curly bracket 10 close curly bracket,
{24}
open curly bracket 24 close curly bracket
{25}
open curly bracket 25 close curly bracket
{36}
The solution set of the equation is {26}
What is Set?Set is a collection of well defined objects.
Given,
The equation is represented by the sentence, "56 of a number is 30."
Replacement set for an equation is {10, 24, 25, 36}.
We need to find the solution set of the equation
"56 of a number is 30"
Fifty six of a number is thirty
56-30
26
Hence, the solution set of the equation is {26}
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PLEASE HELP, WILL GIVE BRAINLIEST! Help and explain, please! Thank you!
Answer:
56 cents
Step-by-step explanation:
cost/amount=price
4/2.24=0.56
5.6/10=0.56
6.72/12=0.56
Determine the smallest integer value of x in the solution of the following inequality.
5x7-1
The smallest integer value of x in the solution of the following inequality x is strictly less than 2 or x ∈ (-∞, 2)
What are inequalities?Inequalities are statements that are represented as comparison between two or more numbers or algebraic expressions.(strictly less, strictly great, greater, lesser)
Given that the inequality 5x - 7 < 2x - 1
Solving the given equation:
5x - 7 < 2x - 1
5x - 7 - 2x < 2x - 1 - 2x
3x - 7 < -1
3x - 7 + 7 < -1 + 7
3x < 6
x < 2
Therefore, We conclude that x is strictly less than 2.
Hence x ∈ (-∞, 2)
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Use a Riemann sum with 4 rectangles of equal width to approximate the area between y=3x^(2)+1 and the x-axis on the interval -1,5. Use the left -hand endpoint of each subinterval.
The approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.
We can approximate the area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 using a Riemann sum with 4 rectangles of equal width. The left-hand endpoint of each subinterval will be used.
The width of each rectangle is the length of the interval (5-(-1)) divided by the number of rectangles (4). Therefore, the width of each rectangle is
(5-(-1))/4 = 6/4 = 1.5.
Since we are using the left-hand endpoint of each subinterval, the x-values of the left-hand endpoints of the rectangles are
-1, -1+1.5
-1+1.5+1.5
-1+1.5+1.5+1.5 = -1+4.5=3.5
The height of each rectangle is determined by the value of y at the corresponding x-value.
Therefore, the heights of the rectangles are
3(-1)^2+1=2
3(-1+1.5)^2+1=7.125
3(3.5)^2+1=35.125
3(3.5+1.5)^2+1=46.875
The area of each rectangle is the product of its width and height, so the areas of the rectangles are
2*1.5=3
7.125*1.5=10.6875
35.125*1.5=52.6875
46.875*1.5=70.3125.
Therefore, the approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.
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what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
Ratio of the area of a square inscribed in a semicircle with radius 'r' to the area of a square inscribed in a circle with radius 'r' is equal to 2: 5.
As given in the question,
Let ABCD be the square with side 'a' inscribed in a semicircle with radius 'r'.
'O' be the center of the semicircle.
'M' be the midpoint of AB such that MB = a/2
Join OM, OB and OM ⊥ AB
OB = r
OM = BC = a
In ΔOMB.
OB² = OM² + MB²
⇒ r² = a² + (a/2)²
⇒r² = 5a²/4
⇒a² = 4r²/5
Area of the square inscribed in a semicircle = a²
= 4r²/5
Let PQRS be the inscribed in a circle with side 'x'
Diagonal of the square inscribed in a circle = 2r
In ΔPQR,
PR = diagonal
= 2r
PQ = QR = x
PR² = PQ² + QR²
⇒(2r)² = x² + x²
⇒x² = 4r² /2
⇒x² = 2r²
Area of the square inscribed in a circle = x²
= 2r²
Ratio of the area of the square inscribed in ( semicircle to the : circle )
= 4r²/5 / 2r²
= 2 / 5
= 2 : 5
Therefore, ratio of the area of the squares inscribed in a semicircle to the circle is 2 : 5.
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Paul buys a ping pong table that has an original price of $350. He uses a coupon code to get a 20% discount off of the original price. He is then charged a 6% tax on the discounted price. What is the final cost for Paul's ping pong table?
The final cost for Paul's ping pong table will be;
⇒ $296.8
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The original price of ping pong table = $350
And, He uses a coupon code to get a 20% discount off of the original price. He is then charged a 6% tax on the discounted price.
Now,
Since, The original price of ping pong table = $350
And, He uses a coupon code to get a 20% discount off of the original price.
Hence, The discounted price = 20% of $350
= 20/100 × 350
= $70
So, The price of ping pong table = $350 - $70
= $280
And, He is then charged a 6% tax on the discounted price.
So, We get;
The tax price = 6% of $280
= 6/100 × $280
= $16.8
Thus, The final price for Paul's ping pong table = $280 + $16.8
= $296.8
Therefore, The final cost for Paul's ping pong table will be;
⇒ $296.8
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The length of a hadow of a building i 15 m. The ditance from the top of the building to the tip of the hadow i 25 m. Find the height of the building. If neceary, round your anwer to the nearet tenth
Answer:
The height of the building is 20 meters
Step-by-step explanation:
What is Pythagoras theorem ?The Pythagoras Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
[tex]c^{2}=a^{2}+b^{2}[/tex]
Where c is the hypotenuse , a is perpendicular length , b is base
Length of the shadow of a building b = 15 m.
The distance from the top of the building to the tip of shadow c = 25 m
Let us assume the Height of the building to be = a
According to the pythagoras theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
[tex]25^{2}=a^{2}+15^{2}[/tex]
[tex]a^{2} = 25^{2}-15^{2}[/tex]
[tex]a^{2}[/tex] = 625-225
[tex]a^{2}[/tex] = 400
a = 20 meters
The height of the building is 20 meters
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what is the x-coordinate of the point that divides the directed line segment from k to j into a ratio 1:3 -1 3 7 11
The x-coordinate of the point that divides the directed line segment from k to j into a ratio 1:3 is given as follows:
x = 7.
How to obtain the x-coordinates?The direction of the segment is given as follows:
K to J.
The desired point divided the directed line segment from k to j into a ratio 1:3, hence the equation involving proportions is given as follows:
P - K = 1/4(J - K).
This equation is used to obtain both the x-coordinate and the y-coordinate of the point.
The x-coordinates of the points are given as follows:
Point P: x.Point K: 9.Point J: 1.Hence the x-coordinate of the segment is obtained as follows:
x - 9 = 1/4(1 - 9)
x - 9 = -2
x = -2 + 9
x = 7.
Missing InformationThe segment is given by the image shown at the end of the answer.
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A construction company is considering submitting bids for two contracts. The company estimates that it has a 20\%20%20, percent chance of winning any given bid. Here is the probability distribution of x=x=x, equals the number of bids the company wins:.
Where the variance is 0.32, the mean is 0.40, and there are provided sets of probabilities, the standard deviation will be 0.566.
What is standard deviation?The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a high standard deviation are spread out from the mean, whereas those with a low standard deviation are grouped together close to the mean.
Here,
mean=0.4
variance=(Xn-mean)².P(x)n
=(0-0.4)²*(0.64)+(1-0.4)²*(0.32)+(2-0.4)²*0.04
variance=0.32
Standard deviation=√(variance)
=√0.32
=0.566
The standard deviation will be 0.566 where variance in 0.32 and mean is 0.40 and given sets of probability.
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Drag and drop the answer into the box to match each point to its coordinates.
The required Co-ordinates are A(-0.5, -0.25), B(-2.5, 1.5) and C(0.25, 0.5).
How to calculate points on the graph?To diagram a point, first find its situation on the x-axis, then track down its area on the y-hub, lastly plot where these meet. The middle place of the chart is known as the origin and is composed as the point (0, 0) since it's situated at the no point on the x-axis and the no point on the y-axis.
What are Co-ordinates ?The distance of a point from y-hub scaled with the x-hub is called abscissa or x direction of the point. The distance of a point from x-pivot scaled with the y-hub is called ordinate. The abscissa and ordinate all together are called organizes.
According to question:Now we find the co-ordinates of points on the graph,
Point A(-0.5, -0.25)
Point B(-2.5, 1.5)
And
Point C(0.25, 0.5)
Thus, required points are A(-0.5, -0.25), B(-2.5, 1.5) andC(0.25, 0.5).
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the ____ of a triangle is a segment that connects the midpoints of two side of the triangle called
Answer:
midsegment
Step-by-step explanation:
hope it helps!
in math, a statement that shows that two expressions are equal.
Answer:
= this is that two expression two equal numbers
If y varies inversely as x and x is 6 when y is 13, what is x when y is 8? a. 9.75 b. 3.69 c. 0.27 d. 6.5
If y fluctuates inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
Define the term inverse proportion?When one variable declines, the others also decline in the same ratio. When two variables move in opposite directions, one variable reduces as another increases and the other increases as another variable lowers, the variables are said to be inversely proportional. Direct proportion is in opposition to it.Inverse variation is demonstrated by the following equation when two quantities, x and y, are in inverse proportion:-
x y = x1 y1
Now, if x is 6 when y is 13 and y varies inversely with x, then at y =8,
Thus,
x × 8 = 6× 13
x = (6×13)/8
x = 9.75
As a result, if y varies inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
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If 1 liter is approximately equal to 1.06 quarts, about how many quarts are in 28.5 liters
Answer:
About 30.21 quarts
Step-by-step explanation:
[tex]q=(28.5)(1.06)=30.21[/tex]
Hope this helps
A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Which of the following tests is most appropriate?
analysis of variance
The correct answer is analysis of variance.
Given that,
Which ethnic group visits movie theaters most frequently That is the question being asked by a researcher. Metric is the dependent variable.
To find : Which of the following tests is most appropriate
What is ANOVA ?
Analysis of variance (ANOVA) is a statistical technique for examining variations in means. It consists of a number of statistical models and the estimating techniques they require. The statistician Ronald Fisher is credited with creating the ANOVA. According to the law of total variance, which is the foundation of ANOVA, the observed variance in a given variable is divided into components that can be attributed to various causes of variation. ANOVA generalizes the t-test beyond two means by offering a straightforward statistical test for the equality of two or more population means. In other words, the ANOVA is employed to compare two or more means.
Therefore, the correct answer is analysis of variance.
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