(a) The likelihood function for a random sample X1, X2, ..., Xn from the distribution with pdf f(x;θ) is given by:
L(θ|x1, x2, ..., xn) = ∏i=1^n f(xi;θ)
For the one-parameter exponential family of distributions, the pdf is given by:
f(x;θ) = exp[A(θ)B(x) + C(x) + D(θ)]
Therefore, the likelihood function can be written as:
L(θ|x1, x2, ..., xn) = exp[∑i=1^n A(θ)B(xi) + ∑i=1^n C(xi) + nD(θ)]
(b) If the likelihood function can be expressed as the product of a function which depends on θ and which depends on the data only through a statistic T(x1, x2, ..., xn), and a function that does not depend on θ, then T is a sufficient statistic for θ.
In the one-parameter exponential family of distributions, we can write the likelihood function as:
L(θ|x1, x2, ..., xn) = exp[nA(θ)B(T) + nC(T) + nD(θ)]
where T = T(x1, x2, ..., xn) is a statistic that depends on the data only and not on θ.
Comparing this to the general form, we see thatthe function that depends on θ is exp[nA(θ)B(T) + nD(θ)], and the function that does not depend on θ is exp[nC(T)]. Therefore, T is a sufficient statistic for θ.
To show that B(x) is a sufficient statistic for θ in the one-parameter exponential family, we need to show that the likelihood function can be written in the form:
L(θ|x1, x2, ..., xn) = h(x1, x2, ..., xn)g(B(x1), B(x2), ..., B(xn);θ)
where h(x1, x2, ..., xn) is a function that does not depend on θ, and g(B(x1), B(x2), ..., B(xn);θ) is a function that depends on θ only through B(x1), B(x2), ..., B(xn).
Starting with the likelihood function from part (a):
L(θ|x1, x2, ..., xn) = exp[∑i=1^n A(θ)B(xi) + ∑i=1^n C(xi) + nD(θ)]
Let's define:
h(x1, x2, ..., xn) = exp[∑i=1^n C(xi)]
g(B(x1), B(x2), ..., B(xn);θ) = exp[∑i=1^n A(θ)B(xi) + nD(θ)]
Now we can rewrite the likelihood function as:
L(θ|x1, x2, ..., xn) = h(x1, x2, ..., xn)g(B(x1), B(x2), ..., B(xn);θ)
which shows that B(x1), B(x2), ..., B(xn) is a sufficient statistic for θ in the one-parameter exponential family.
(c) If the sample consists of iid observations from the Uniform distribution on the interval (0, θ), then the pdf of each observation is:
f(x;θ) = 1/θ for 0 < x < θ
The likelihood function for a random sample X1, X2, ..., Xn from this distribution is:
L(θ|x1, x2, ..., xn) = ∏i=1^n f(xi;θ) = (1/θ)^n for 0 < X1, X2, ..., Xn < θ
To find a sufficient statistic for θ, we need to express the likelihood function in the form:
L(θ|x1, x2, ..., xn) = h(x1, x2, ..., xn)g(T(x1, x2, ..., xn);θ)
where T(x1, x2, ..., xn) is a statistic that depends on the data only and not on θ.
Since the likelihood function only depends on the maximum value of the sample, we can define T(x1, x2, ..., xn) = max(X1, X2, ..., Xn) as the maximum of the observed values.
The likelihood function can then be written as:
L(θ|x1, x2, ..., xn) = (1/θ)^n * I(x1, x2, ..., xn ≤ θ)
where I(x1, x2, ..., xn ≤ θ) is the indicator function that equals 1 if all the observed values are less than or equal to θ, and 0 otherwise.
We can see that the likelihood function depends on θ only through the term 1/θ, and the function I(x1, x2, ..., xn ≤ θ) depends on the data only and not on θ. Therefore, T(x1, x2, ..., xn) = max(X1, X2, ..., Xn) is a sufficient statistic for θ in the Uniform distribution on the interval (0, θ).
Marcus asked 10 people at a juggling festival what age they were when they started to juggle
Question
Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]n = 10[/tex]
Required
The median interval
The question is incomplete, as the required data is not given.
To solve this question, I will use the following assumed dataset.
[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]
First, calculate the median position.
[tex]Median = \frac{n+1}{2}\ th[/tex]
[tex]Median = \frac{10+1}{2}\ th[/tex]
[tex]Median = 5.5\ th[/tex]
This implies that the median is the mean of the 5th and 6th data
So, we have the interval to be.
[tex]Median = [5th, 6th][/tex]
[tex]Median=[21,22][/tex]
Generally, the median of 10 data set is located at interval 5 to 6
Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)
Answer:
y - 6 = -1 (x+5)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1} \\[/tex]. Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:
[tex]m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1[/tex]
So, the slope of the line is -1.
2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope of the line, substitute -1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:
[tex]y-6 = -1(x+5)[/tex]
NO LINKS PLZ, BUT I RLLY NEED HELP!
Answer:
Step-by-step explanation:
b
A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 450 dollars and a standard deviation of 30 dollars. 20 per cent of the BBQs would cost more than what price? Select from the answers below.
(a)424.8 (b)475.2 (c)430 (d)492
Answer: (a) $424.8
Step-by-step explanation:
Help, I don't want to lose my answer streak.
Answer:
[tex]4\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]
Answer:
leon's older brother is 4 5/12 feet tall
Step-by-step explanation:
4 3/4 - 1/3
= 4 5/12
it is now twenty-one minutes to ten. what time will it be in 5 hours and 17 minutes? write your answer using numbers and a colon (for example, 11:58).
The time after 21 minutes from 9:39 is 2:56am.
Given that it is now twenty-one minutes to ten, we need to determine the time in 5 hours and 17 minutes.
To find the answer, we can add 5 hours and 17 minutes to the current time, which is 9:39 PM. Let's first convert the hours to minutes:5 hours = 5 x 60 = 300 minutes.
Then, add 300 minutes and 17 minutes:300 minutes + 17 minutes = 317 minutes.
Since there are 60 minutes in an hour, we need to divide 317 by 60 to determine the number of hours:317 / 60 = 5 with a remainder of 17.
Therefore, the time in 5 hours and 17 minutes will be 2:56 AM.
To check our answer, we can work backward:
Start with 2:56 AM and subtract 5 hours and 17 minutes:2:56 AM - 5 hours = 9:56 PM9:56 PM - 17 minutes = 9:39 PMAs expected, we arrived back at the original time of 9:39 PM. Therefore, the final answer is 2:56.
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Triangle triangle A^ prime B^ prime C^ prime is the image of triangle ABC under a dilation What is the scale factor of the dilation
The scale factor of a dilation is the ratio of the corresponding side lengths of the image triangle to the original triangle. In this case, the image triangle is triangle A' B' C' and the original triangle is triangle ABC.
To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's denote the lengths of the corresponding sides as follows:
Side AB corresponds to side A'B'
Side BC corresponds to side B'C'
Side CA corresponds to side C'A'
The scale factor is then given by:
Scale factor = Length of corresponding side in image triangle / Length of corresponding side in original triangle
To find the scale factor, you can calculate the ratio of the corresponding side lengths. For example, if the length of AB is 4 units and the length of A'B' is 8 units, then the scale factor would be 8/4 = 2.
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38. The vertices of a trapezoid are points (0, a), (0,0), (6,0), and (c, a). Find the area in terms
of a, b, and c.
Answer:
(0,6), (6,0)
Step-by-step explanation:
Answer:
Whatttttttttttttttttt
Change from rectangular to spherical coordinates. (Let rho ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.)
(a)
(0, −5, 0)
(rho, θ, ϕ) =
In spherical coordinates (ρ, θ, ϕ), the point (0, -5, 0) can be represented as (5, π/2, π/2).
To convert from rectangular coordinates to spherical coordinates, we use the following formulas:
ρ = √(x² + y² + z²)
θ = arctan(y / x)
ϕ = arccos(z / √(x² + y² + z²))
In this case, since the point lies on the negative y-axis, the x-coordinate is 0, and the y-coordinate is -5. Therefore, we have:
ρ = √(0² + (-5)² + 0²) = √25 = 5
Since the point lies in the negative y-axis, the angle θ is π/2.
Since the point lies on the xz-plane, the z-coordinate is 0. Therefore, we have:
ϕ = arccos(0 / √(0² + (-5)² + 0²)) = arccos(0 / 5) = arccos(0) = π/2
Combining these values, the point (0, -5, 0) in rectangular coordinates is equivalent to (5, π/2, π/2) in spherical coordinates.
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You randomly choose a marble from a jar. The jar contains 4 red marbles, 10 blue marbles, 7 green marbles, and 6 yellow marbles. Find the probability of the event. Not choosing a blue marble.
Answer:
17/27
Step-by-step explanation:
Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).
The probability of not choosing a blue marble is 17/27.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of red marbles = 4
Number of blue marbles = 10
Number of green marbles = 7
Number of yellow marbles = 6
The event is the probability of not choosing a blue marble is
⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]
⇒ [tex]\frac{4+7+6}{27}[/tex]
⇒ [tex]\frac{17}{27}[/tex]
Hence we can conclude that the the probability of not choosing a blue marble is 17/27.
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What is the area of the triangle?
24
7
25
units2
A health psychologist wants to test the effectiveness of a new stress-reduction method. In the general population, stress level is normally distributed with μ = 40 and σ = 10. 40 randomly selected people are trained in the method; the mean score afterward is 36.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1:
Population 2:
Research hypothesis:
Null hypothesis:
7. Determine the characteristics of the comparison distribution.
8. Determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
The cutoff sample score is therefore:40 - 2.326(1.5811) ≈ 36.59
The research hypothesis and null hypothesis about the populations can be restated as follows:Population 1: The population of people who have not received the new stress-reduction method training.Population 2: The population of people who have received the new stress-reduction method training.Research hypothesis: The new stress-reduction method training has reduced stress levels in the population that has received it compared to the population that has not.Null hypothesis: The new stress-reduction method training has not reduced stress levels in the population that has received it compared to the population that has not.7. The comparison distribution in this case is the distribution of means from samples of the population that has not received the new stress-reduction method training. This distribution has a mean (μ) equal to the population mean of 40 and a standard deviation (σ) equal to the population standard deviation divided by the square root of the sample size, which is σ/√n = 10/√40 = 1.5811.8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01, we need to find the z-score corresponding to a probability of .01 in the right tail of the distribution. This is given by:z = invNorm(0.99) ≈ 2.326Therefore, if the sample mean of the population that has received the new stress-reduction method training is more than 2.326 standard errors below the mean of the comparison distribution (which is 40), the null hypothesis can be rejected at the 0.01 level of significance.
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6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. The Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. To determine the characteristics of the comparison distribution.
The comparison distribution is the distribution of sample means if we drew all possible samples of the same size from the population of interest.
In this case, we have a sample of 40 people who were trained in the stress-reduction method, so the comparison distribution will be a distribution of sample means of size 40 from the population of people who follow the stress-reduction method.
The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
To find the cutoff sample score (or Z score), we need to calculate the Z score of the sample mean (36) using the formula:
Z = (X - μ) / (σ / sqrt(n))
Z = (36 - 40) / (10 / sqrt(40))
Z = -2.52
The cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01 is the Z score that corresponds to a probability of .01 in the upper tail of the distribution, which is equal to 2.33.
Therefore, if the Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
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how many different four-digit ID tags can be made if repeats are allowed
Answer:
4!Explanation:
4! = 4×3×2×1 = 24
here's an example:
123412431324134214231432213421432314234124132431312431423214324134123421412341324213423143124321Prove or disprove, using any method, that if /25 Q, then it is the case that 25 – 17 € Q.
The statement if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q is false.
To disprove the statement, we need to provide a counter example where [tex]\sqrt{25}[/tex] ∉ Q (irrational) and [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∉ Q (also irrational).
Let's consider [tex]\sqrt{25}[/tex] = 5, which is a rational number since it can be expressed as a ratio of two integers (5/1).
In this case, [tex]\sqrt{25}[/tex] ∉ Q is false since it is a rational number.
Furthermore, [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] = 5 - [tex]\sqrt{17}[/tex] is also irrational since it cannot be expressed as a ratio of two integers.
Therefore, we have found a counterexample that disproves the statement, showing that if [tex]\sqrt{25}[/tex] ∉ Q, then it is not necessarily the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.
Hence, the statement is false.
Question: Prove or disprove, using any method, that if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.
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please answer the question
Answer:
I think it is 25÷8
Step-by-step explanation:
this is because the circumference is found by π multiplied by the diameter. So the inverse would be the circumference divided by the diameter.
Please help!!
A school is constructing a rectangular play area against an exterior wall of the school
building. It uses 120 feet of fencing material to enclose three sides of the play area.
Answer:
Step-by-step explanation:
Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.
120 = L + 2W
Where
LW = area.
Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60
On substituting, we have
A = LW = (120 - 2W) W
From the first equation, making L the subject of the formula, we have this
L = 120 - 2W, which then we substituted above.
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
The required length of the rectangular garden is 60 feet
Area of rectangular shapeAccording to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
Hence the required length of the rectangular garden is 60 feet
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Which is NOT true?
A 9 + 4 = 17 - 4
B 8 + 7 = 14 + 3
C 11 = 19 - 8
D 5 + 8 = 20 - 7
Answer:
B is not true
Step-by-step explanation:
8+7= 15 and 14+3= 17
15 is not equal to 17
Answer:
B is the one equation that is NOT true.
Step-by-step explanation:
A: 9+4 is 13, and 17-4 is 13 as well. This equation is true, 13=13.
B: 8+7 is 15, and 14+3 is 17. This equation is false, because 15 is not equal to 17. Although we have our answer, we need to still check the other equations.
C: 11 is, well, 11, because nothing changed on that side of the equation. 19-8 is 11, so this is true because 11=11.
D: 5+8 is 13, and 20-7 is 13. This equation is also true, because 13=13.
The only equation that is not true, is B. (8+7 = 14+3)
For 1-4, a line has the points (-2,-9),
(3, 1), and (6, 7). Find the polnts for the
translation described.
1. 6 units to the left
2. 3 units down
3. 5 units to the right
4 2 units up
Answer:
3 units down
Step-by-step explanation:
got it right on edg
Use the z -score formula, z=x−μσ z = x − μ σ , and the information below to find the mean, μ . Round your answer to one decimal place, if necessary.
z = 2.25 x = 14.6 0 =3.6
The mean value is 6.5.
Given, z = 2.25, x = 14.6, σ = 3.6
The formula to calculate the z-score is,
z-score, z = (x - μ) / σOn
substituting the given values in the above formula, we get
2.25 = (14.6 - μ) / 3.6
Multiplying both sides by 3.6, we get,
2.25 * 3.6 = 14.6 - μ8.1 = 14.6 - μ
Subtracting 14.6 from both sides, we get,
-6.5 = -μOn multiplying both sides by -1, we get,
μ = 6.5
Hence, the mean value is 6.5.
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The decimal place z -score formula, z=x−μσ z = x − μ σ the mean (μ) is 6.5.
To find the mean (μ) using the z-score formula the Solve for μ
z = (x - μ) / σ
substitute the given values into the equation
2.25 = (14.6 - μ) / 3.6
solve for μ:
2.25 × 3.6 = 14.6 - μ
8.1 = 14.6 - μ
To isolate μ, subtract 14.6 from both sides:
8.1 - 14.6 = -μ
-6.5 = -μ
multiplying both sides by -1 gives
6.5 = μ
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Which is greater 52,800 cm or 1 km?
Answer:
1 km
Step-by-step explanation:
According to the unit of conversion in every 1 kilometer, there is a total of 100 000 centimeters. Now, the given value of centimeters is equals to 52 800 => 1 km = 100 000 cm => 52 800 cm is less than the value of 100 000 cm which is equivalent to 1 km. Thus, the given is not correct.
find the surface area to the nearest tenth
Step-by-step explanation:
Surface Area of Figure = Area of 4 triangular sides + Area of Base
=
[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]
Two ovens have measurements as shown. Which oven has a greater volume? How much greater is
its volume?
The question is incomplete:
Two ovens have measurements as shown. Which oven has a greater volume? How much greater is its volume?
The image with the information is below.
Answer:
-Oven B has a greater volume.
-Its volume is greater by 768 in³.
Step-by-step explanation:
First, you have to calculate the volume of each oven by multiplying the area of the base by the height:
Oven A: 576 in²*15 in= 8640 in³
Oven B: 672 in²*14 in= 9408 in³
Now, you have to calculate the difference between the volumes:
9408-8640=768
According to this, the answer is that oven B has a greater volume. Its volume is greater by 768 in³.
a graph represents the perimeter y in units for an equilateral triangle
If the graph represents the perimeter (y) in units for an equilateral triangle, we can determine the relationship between the perimeter and the side length of the triangle.
In an equilateral triangle, all three sides are equal in length. Let's denote the side length of the equilateral triangle as x.
The perimeter (P) of an equilateral triangle is given by the formula:
P = 3 * x
Therefore, the relationship between the perimeter (y) and the side length (x) of the equilateral triangle is:
y = 3x
So, if the graph represents the perimeter (y) in units for an equilateral triangle, it would be a linear function with a slope of 3 and the side length (x) as the independent variable.
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help pleaseee!! i’ll give u most brianliest
PLz hlep will mark brain list
Answer:
20
Step-by-step explanation:
Find the difference of the smallest value and the largest value.
Answer:
30 minus 10 then the range is 20
y=(2.5)^x graph and match function
Answer:
Step-by-step explanation:
Dot plot A is the top plot. Dot plot B is the bottom plot.
According to the dot plots, which statement is true?
The mean of the data in dot plot A is less than the
mean of the data in data plot B.
The median of the data in dot plot A is greater than the
median of the data in dot plot B.
The mode of the data in dot plot A is less than the
mode of the data in dot plot B.
The range of the data in dot plot A is greater than the
range of the data in dot plot B.
Please help I’m giving BRAINLIEST
Answer:
The median of plot A is greater that the median of plot B
Step-by-step explanation: the median on plot A is 45 and the median on plot B is 15
1)The mean of the data in plot A is greater than the
mean of the data in plot B.
2) The median of the data in plot A is greater than the
median of the data in dot plot B.
3) The range of the data in plot A is greater than the
range of the data in plot B.
What is the median?
The median is the middle number in a sorted, ascending, or descending, list of numbers.
Let us arrange the data of plot A in ascending order:
30,35,35,40,40,40,40,45,45,45,45,50,55,55,60
Number of observations = 15
Mean of the plot A = 44
Median will be the middle observation i.e. 8th observation i.e. 45
Let us arrange the data of plot A in ascending order:
5,5,5,10,10,10,10,15,15,15,20,20,25,30,35
Number of observations = 15
Mean of the plot B = 15.33
Median will be the middle observation i.e. 8th observation i.e. 15
Therefore,1)The mean of the data in plot A is greater than the
mean of the data in plot B.
2) The median of the data in plot A is greater than the
median of the data in dot plot B.
3) The range of the data in plot A is greater than the
range of the data in plot B.
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Determine the p-value for the two-tailed t-test with df = 19 (remember, H_1: µ ≠ µo) and sample t = -0.36. At a significance level of α = .01 do you reject or retain the null hypothesis?
The p-value for the two-tailed t-test with degrees of freedom (df) = 19 and a sample t-value of -0.36 is greater than the significance level of α = 0.01. Therefore, we retain the null hypothesis.
In a two-tailed t-test, the null hypothesis (H₀) states that there is no significant difference between the population mean (µ) and a hypothesized mean (µo). The alternative hypothesis (H₁) states that the population mean is not equal to the hypothesized mean.
To determine the p-value, we compare the absolute value of the sample t-value (-0.36 in this case) with the critical t-value for the given degrees of freedom (df = 19). Since the sample t-value falls within the acceptance region, we find the probability of obtaining a t-value as extreme as -0.36 (or more extreme) assuming the null hypothesis is true.
If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. However, if the p-value is greater than the significance level, we retain the null hypothesis. In this case, since the p-value is greater than 0.01, we do not have sufficient evidence to reject the null hypothesis. Therefore, we retain it.
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Which expression is equivalent to 21x + 9 - 3x? A. 9(2x - 1) B. 9(x + 1) C. 9(2x + 1) D. 18(x + 1)
Answer: C
Step-by-step explanation:
21x+9-3x = 18x + 9
If you factor out the 9, you would be left with
9 (2x+1)
Answer: A. 9(2x - 1)
Step-by-step explanation:
combine like terms
21x+9-3x
21x-3x
18x+9
Factor the expression
factor out 9 from the expression
you get 9(2x - 1)
Consider the system of equations below. Explain how you could use multiplication to help eliminate one of the variables.
x−5y=13
4x−3y=1
Answer:you cross multiply
Step-by-step explanation:
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