Answer:
$225
Step-by-step explanation:
-RevPar is defined as the room revenue divided by the number of rooms available:
[tex]RevPar=\frac{Room \ Revenue}{Rooms \ Available}[/tex]
-The average number of rooms sold per day in the two days is:
[tex]mean =\frac{450}{2}\\\\=225\ rooms[/tex]
The PevPar can then be calculated as:
[tex]RevPar=\frac{Room \ Revenue}{Rooms \ Available}\\\\=\frac{ADR\times mean occupancy}{Rooms \ Available}\\\\=\frac{300\times 225}{300}\\\\=225[/tex]
Hence, the PevPar is $225
Below are two parallel lines with a third line intersecting them. What is x
Answer:
136=x
Step-by-step explanation:
When an angle is shown, the one opposite of it is equal to the forst equation. The bottom angles are equal to 360ñ so if you take 46x2=92. Subtract 92 by 360 to get 268. Divide it by 2 to get one of the bigger angles, which is 134 degrees. And as for the top, one angle on the bottom is equal to the same spot on the top. so, 136=x
Answer :
x = 134°
Step by step :
46° + x = 180°
x = 180° - 46°
x = 134°
Claim: Students should be required to take at least one online class.
Counterclaim: Some students can focus better when they are in a traditional classroom setting.
Which statement is the best rebuttal to the counterclaim given?
(A). When working on an online class, students have more freedom to choose an environment that is best for them.
(B). A traditional classroom is the best environment for learning, but an online class can be good for students too.
(C). Students should only be taught in a traditional classroom environment, because it works best for everyone.
Answer:
A. when working on an online class students have more freedom to choose an environment in which they are most comfortable
Step-by-step explanation:
some students do better at home some do better in a traditional setting but being online lets you change your setting to anywhere with online access
How do the areas of triangle ABC and DEF compare?
O The area of ABC is 1 square unit less than the area of
ADEF
O The area of AABC is equal to the area of ADEF.
O The area of ABC is 1 square unit greater than the
area of ADEF.
O The area of ABC is 2 square units greater than the
area of ADEF.
Answer:
C: The area of ABC is 1 square unit greater than the
area of ADEF
Step-by-step explanation:
Due to the area of triangle ABC and triangle DEF, the ABC triangle has dimensions that are 1 square unit greater that the area of ADEF. This is because the lines have different lengths. Good Luck on the Rest of Your Questions!!
Answer: C
Step-by-step explanation:
Answer true or false. If false, explain briefly. a) Some of the residuals from a least squares linear model will be positive and some will be negative. b) Least squares means that some of the squares of the residuals are minimized. c) We write ModifyingAbove y with caret to denote the predicted values and y to denote the observed values.
a) True. Some residuals will be positive and some will be negative. b) True. Least squares minimizes the squares of the residuals. c) False. y with a caret denotes predicted values.
Explanation:a) True. Some of the residuals from a least squares linear model will be positive and some will be negative. Residuals measure the difference between the observed values and the predicted values, and they can be positive if the observed value is higher than the predicted value, or negative if the observed value is lower.
b) True. Least squares regression aims to minimize the sum of squared residuals. By minimizing the squares of the residuals, we ensure that the line of best fit is as close as possible to the data points.
c) False. We write y with a caret (^) to denote the predicted values and y without a caret to denote the observed values.
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Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for Inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month? 32 +1.645,8908 32 + 1.9620 0.64 + 1.282,16.620.) © 264 265 CHAT 0.04 + 1.00, layanan
Answer:
0.64 ± 0.1117 or
[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(0.36)}{50}}[/tex]
Step-by-step explanation:
Sample size (n) = 50
Z-score for a 90% confidence interval (z) = 1.645
Proportion of students that read at least one book (p):
[tex]p=\frac{32}{50}=0.64[/tex]
The confidence interval is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Applying the given data:
[tex]0.64\pm 1.645*\sqrt{\frac{0.64*(1-0.64)}{50}}\\ 0.64\pm 0.1117[/tex]
The confidence interval is 0.64 ± 0.1117
The 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].
Given information:
From a random sample of 50 (n) students, Alma found that 32 students read at least 1 book last month.
Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book.
It is required to find the 90 percentage confidence interval for the proportion of all students in her district who read at least 1 book last month.
Now, from tha table, the z-score of 90 percent confidence level is,
[tex]z=1.645[/tex]
The probability p for the proportion of students who read atleast one book is,
[tex]p=\dfrac{32}{50}\\p=0.64[/tex]
So, the 90 percent confidence interval will be calculated as,
[tex]p\pm z\sqrt{\dfrac{p(1-p)}{n}}=0.64\pm 1.645\times \sqrt{\dfrac{0.64(1-0.64)}{50}}\\=0.64\pm 0.11178[/tex]
Therefore, the 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month is [tex]0.64\pm 0.11178[/tex].
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A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262, .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
Final answer:
The point estimate for the proportion of college students who prefer drink A is found by averaging the lower and upper bounds of the 95% confidence interval, which yields an estimate of 0.442 or 44.2%.
Explanation:
The point estimate for the true proportion of college students who prefer drink A is the midpoint of the 95% confidence interval. To find the point estimate, you sum the lower and upper bounds of the interval and divide by 2. In this case, the confidence interval is (.262, .622). The calculation for the point estimate is (0.262 + 0.622) / 2, which equals 0.442. Therefore, the point estimate is 0.442, which means that approximately 44.2% of college students prefer drink A.
HELP PLEASEEEE! I kinda need this done asap so can anyone explain it to me? :)
Answer:
The Answer is 25.5 in
Step-by-step explanation:
What you basically do is
17² * 17²= 289
19² * 19²= 361
Then add 289+361=650
Then u have to Divide
Then you should get 25.495
Then Round to the nearest Tenth and you Get (25.5 in)
Hope This was Right
Answer:
25.49
Step-by-step explanation:
To find the hypotenuse for right triangles, we use the Pythagorean Theorem or
[tex]A^{2} +B^{2} = C^{2}[/tex]
Keep in mind we only use this for right triangles
With that in mind, lets solve for side c
[tex]A^{2} + B^{2} = C^{2} \\19^{2} +17^{2} = C^{2} \\(19*19) + (17*17) = C^{2} \\361+ 289 = 650\\C^{2} = 650\\\sqrt{650} = C\\C = 5\sqrt{26} or 25.49[/tex]
Hope This Helps!
Find BC
(round to the nearest hundredth)
Given:
In ΔABC, ∠C = 90°, ∠A = 50° and AB = 3 unit.
To find the value of BC.
Formula:
By Trigonometric Ratio we get,
[tex]sin \ \theta=\frac{opposite}{Hypotenuse}[/tex]
Now,
With respect to θ = 50°, AB is the hypotenuse and AB is the opposite side.
So,
[tex]sin \ 50^{\circ}=\frac{BC}{AB}[/tex]
[tex]sin \ 50^{\circ}=\frac{BC}{3}[/tex]
[tex]BC = 3 \times sin 50^{\circ}[/tex]
[tex]BC = 2.298 = 2.3[/tex] (approx)
Hence,
The value of BC is 2.3 units.
49w = −8
what is the value of w
Answer:
w= -0.163265306122449
Step-by-step explanation:
49w = -8
divide both sides by 49
w= -8/49 = -0.163265306122449
check answer by multiplying -0.163265306122449 by 49
49 * -0.163265306122449 = -8
Answer:
w = -8/49
Step-by-step explanation:
49w = −8
Divide each side by 49
49w/49 = -8/49
w = -8/49
nancy bought 7 1/2 gallons of milk for the school cafeteria.she bought only half-gallon containers. how many half gallon containers did she buy
Hi to whoever is reading this. I really need help on breaking down the expression. I am doing this without a calculator and I don’t Know what steps to take to get the answer.
Answer:
A
Step-by-step explanation:
[tex]81[/tex] is [tex]9^2[/tex] which happens to be [tex](3^2)^2[/tex] or [tex]3^4[/tex].
So [tex]\sqrt[4]{81} =3[/tex]
this eliminates options C and D
It can't be option B as both b and c aren't 4th rooted.
A plant grows 12 mm every four months how many centimeters will it grow in one year?
Step-by-step explanation:
One year is 12 months. 12 mm is 1.2 cm.
Write and solve a proportion
1.2 cm / 4 months = x / 12 months
x = 3.6 cm
Tiffany sells cars. She gets an 18% commission. How much will she make on a $ 28,000.00 car?
Answer:
5040$
Step-by-step explanation:
28000 x .18 = 5040
We are given that if Tiffany closes any car on a car she gets 18% as commission. For a car that cost $28,000 her commission will be $5,040
Given data
Commission = 18%
Cost of car = $ 28,000.00
Let us find 18% of $28,000.00
Commission = 18/100* 28,000.00
Commission = 0.18* 28,000.00
Commission = $5,040
Hence her commission will be: $5,040
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A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs.
They sold each ticket for $45.
Let y represent the net profit (in dollars) when they have sold 2 tickets.
Which of the following information about the graph of the relationship is given?
Answer: slope and x-intercept
y-intercept and a point that is not an intercept is the information about the graph of the relationship is given. So, the correct answer is E. y-intercept and a point that is not an intercept
Let's analyze the information given in the problem:
1. The charity organization sold 18 tickets to cover necessary production costs.
2. They sold each ticket for $45.
3. They want to determine the net profit when they have sold 2 tickets.
We are given a specific point on the graph: (x = 2, y = net profit when 2 tickets are sold).
Now, let's calculate the net profit when 2 tickets are sold:
Net profit when 2 tickets are sold = Total revenue - Total production costs
Total revenue = 2 tickets * $45 per ticket = $90
Total production costs = $18 (to cover necessary production costs)
Net profit = $90 - $18 = $72
Now, let's look at the options:
A. Slope and x-intercept: We do not have the slope or the x-intercept of the graph.
B. Slope and y-intercept: We do not have the slope or the y-intercept of the graph.
C. Slope and a point that is not an intercept: We have a point on the graph, but we do not have the slope.
D. x-intercept and y-intercept: We do not have the x-intercept or the y-intercept of the graph.
E. y-intercept and a point that is not an intercept: We have the y-intercept (net profit when 0 tickets are sold, which is $18) and a point on the graph (net profit when 2 tickets are sold, which is $72).
F. Two points that are not intercepts: We have one point on the graph (net profit when 2 tickets are sold, which is $72), but we do not have another point.
So, Based on the information given, the correct option is:
E. y-intercept and a point that is not an intercept
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Correct Question is:
A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs.
They sold each ticket for $45.
Let y represent the net profit (in dollars) when they have sold 2 tickets.
Which of the following information about the graph of the relationship is given?
A. Slope and x- intercept
B. Slope and y-intercept
C. Slope and a point that is not an intercept
D. x-intercept and y intercept
E. y-intercept and a point that is not an intercept
F. Two points that are not intercepts
Find the area of the shaded sector. Round to the nearest tenth and use 3.142 or the pi button on your calculator for pi.
answers: (all answers are squared)
44.0 in2
66.0 in2
263.9 in2
22.0 in2
Given:
Given that the radius of the circle is 12 inches.
The angle of the shaded sector is 210°
We need to determine the area of the shaded sector.
Area of the shaded sector:
The area of the shaded sector can be determined using the formula,
[tex]Area =(\frac{\theta}{360}) \pi r^2[/tex]
Substituting [tex]\theta=210[/tex] and r = 12, we get;
[tex]Area =(\frac{210}{360}) (3.142)(12)^2[/tex]
Simplifying, we get;
[tex]Area =(\frac{210}{360}) (3.142)(144)[/tex]
[tex]Area =263.9 \ in^2[/tex]
Thus, the area of the shaded sector is 263.9 square inches.
Hence, Option c is the correct answer.
Thomas purchased a used vehicle that depreciates under a straight-line
method. The initial value of the car is $7000, and the salvage value is $500. If
the car is expected to have a useful life of another 5 years, how much will it
depreciate each year?
O
A. $1300
O B. $1000
O c. $7000
O D. $5000
Answer: A. $1300
Step-by-step explanation:
The initial value is $7000
The Salvage value is $500
The car will depreciate under a straight-line method, meaning it will lose $6500 value in 5 years.
6500 / 5 = 1300
Find the sum of place value and face value of 7 in 1879523
Answer:
Ok. so the Place value is 70000 and the face value is 7. Face value of a digit in a number is the digit itself.
More clearly, face value of a digit always remains same irrespective of the position where it is located
Place value of a digit in a number is the digit multiplied by thousand or hundred or whatever place it is situated.
Hope this helped.
Step-by-step explanation:
For the data set: 12, 8, 6, 6, 9, 8, 7, 11, 6, “6” is the value for which measure?
In the given data set, 12, 8, 6, 6, 9, 8, 7, 11, 6, the value 6 represents the mode.
We are given the following dataset: 12, 8, 6, 6, 9, 8, 7, 11, 6.
Count the frequency of each number:
12 appears 1 time.
8 appears 2 times.
6 appears 3 times.
9 appears 1 time.
7 appears 1 time.
11 appears 1 time.
The number 6 appears 3 times, more frequently than any other number.
By the definition of mode, it is the value that appears most frequently in a data set.
Since 6 occurs more times than any other number in the list, then it is the mode
Fine the value of d. 2d-5= 17
Answer:
d = 11
Step-by-step explanation:
What are the possible outcomes of flipping a coin once
Answer:
1/2 chances if getting heads 1/2 for getting tails
Answer:
heads or tails
You are given the polar curve r=eθ. (a) List all of the points (r,θ) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of r and limit yourself to 1≤r≤1000 ( note the restriction on r!) and 0≤θ<2π. If two or more points share the same value of r, list those starting with the smallest value of θ. If any blanks are unused,
Answer:
θ [tex]0.75\pi[/tex] [tex]1.75\pi[/tex]
r 10.551 244.151
Step-by-step explanation:
The maximum value for [tex]\theta[/tex] is:
[tex]\theta_{max} = \ln r[/tex]
[tex]\theta_{max} = 2.199\pi\,rad[/tex]
The formula for the slope of the tangent line in polar coordinates is:
[tex]m = \frac{r'\cdot \sin \theta + r \cdot \cos \theta}{r' \cdot \cos \theta - r \cdot \cos \theta}[/tex]
Horizontal tangent lines have a slope of zero. So, the following relation must be satisfied:
[tex]r'\cdot \sin \theta + r \cdot \cos \theta = 0[/tex]
[tex]r'\cdot \sin \theta = - r \cdot \cos \theta[/tex]
[tex]\tan \theta = - \frac{r}{r'}[/tex]
[tex]\tan \theta = -\frac{e^{\theta}}{e^{\theta}}[/tex]
[tex]\tan \theta = -1[/tex]
[tex]\theta = \tan^{-1}(-1)[/tex]
[tex]\theta = \frac{3}{4}\pi + i\cdot \pi[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex].
The maximum value of i is:
[tex]i = \frac{\theta_{max}-\frac{3}{4}\pi }{\pi}[/tex]
[tex]i = \frac{2.199-0.75}{1}[/tex]
[tex]i = 1.449[/tex] ([tex]i_{max} = 1[/tex]).
Then, values are listed below:
θ [tex]0.75\pi[/tex] [tex]1.75\pi[/tex]
r 10.551 244.151
Answer:
{ ( 2.193 , π / 4) , ( 10.551 , 3π / 4) , ( 50.754 , 5π / 4) , ( 244.151 , 7π / 4) }
Step-by-step explanation:
Given:-
- The polar curve has the equation:
r = e^θ
- list the points starting with the smallest value of r such that:
1 ≤ r ≤ 1000 , 0 ≤ θ < 2π.
Find:-
List all of the points (r,θ) where the tangent line is horizontal
Solution:-
- We will first transform the polar curve to cartesian coordinate system using the parametric relations:
x = r*cos (θ)
y = r*sin (θ)
- The tangent line is horizontal when the " dy / dθ " = 0 and " dx / dθ " = 0, so:
x = e^θ*cos (θ) , y = e^θ*sin (θ)
dx / dθ = e^θ*cos (θ) - e^θ*sin(θ)
= e^θ*[cos (θ) - sin(θ)]
dx / dθ = e^θ*[cos (θ) - sin(θ)] = 0,
e^θ = 0 , [cos (θ) - sin(θ)] = 0
e^θ ≠ 0 for the given interval 0 ≤ θ< 2π
cos (θ) - sin(θ) = 0 , tan ( θ ) = 1 - (1st quad and 3rd quad)
θ = { π / 4 , 5π / 4 } , 0 ≤ θ< 2π
- Similarly, evaluate dy/dθ = 0;
dy/dθ = e^θ*cos (θ) + e^θ*sin(θ)
= e^θ*[cos (θ) + sin(θ)]
dy / dθ = e^θ*[cos (θ) + sin(θ)] = 0,
e^θ = 0 , [cos (θ) + sin(θ)] = 0
e^θ ≠ 0 for the given interval 0 ≤ θ< 2π
cos (θ) + sin(θ) = 0 , tan ( θ ) = -1 , (2nd quad and 4th quad)
θ = { 3π / 4 , 7π / 4 } , 0 ≤ θ< 2π
- All possibilities of " θ " over the interval satisfying the a horizontal tangent line to the given polar curve:
θ = { π / 4, 3π / 4 , 5π / 4 , 7π / 4 } , 0 ≤ θ < 2π
- We will plug the evaluated list of values of "θ " in the given polar curve and determine the corresponding values of "r":
r = e^θ
θ = π / 4 , r = e^(π / 4) = 2.193
1: ( r , θ ) = ( 2.193 , π / 4)
θ = 3π / 4 , r = e^(3π / 4) = 10.55072
2: ( r , θ ) = ( 10.551 , 3π / 4)
θ = 5π / 4 , r = e^(5π / 4) = 50.754
3: ( r , θ ) = ( 50.754 , 5π / 4)
θ = 7π / 4 , r = e^(7π / 4) = 244.151
4: ( r , θ ) = ( 244.151 , 7π / 4)
A deck of cards contains 52 cards.two decks are put together and divided among eight players.how many cards does each person get
Answer:
13 cards
Step-by-step explanation:
One deck has 52 cards.
2 decks have 2 * 52 cards, or 104 cards.
104 cards are divided among 8 players.
104/8 = 13
Answer: 13 cards
you start at (6, 8). You move down 6 units and left 1 unit. Where do you end?
State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 80 cars. Taking a random sample of eighty cars is considered sufficiently large for the distribution of the sample proportion to be normally distributed. Would a random sample of 50 cars have been large enough and why?
Answer:
With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to the normal distribution if:
np > 5, n(1-p) > 5
70% of the drivers traveling on a major interstate highway exceed the speed limit.
So p = 0.7.
Would a random sample of 50 cars have been large enough and why?
With n = 50
np = 50*0.7 = 35 > 5
n(1-p) = 50*0.3 = 15 > 5
With n = 50, both conditions(np > 5, n(1-p) > 5) are satisfied, so a random sample of 50 cars would have been large enough.
Using the common denominator what is the equivalent fraction of 1/8
Answer:
2/16
Step-by-step explanation:
1/8 x 2 = 2/16
Both 2 and 16 divide by 8, so one can know this is correct.
Also, both 8 and 16 are divisible by 8, so one can see this is the common denominator.
What is the word form for 355.3 kilograms
Answer:
Three hundred fifty-five and three tenths.
Step-by-step explanation:
The word form for 355.3 kilograms is "Three hundred fifty-five point three kilograms." This representation breaks down the number into its hundreds, tens, ones, tenths, and specifies the unit of measurement, kilograms.
The word form for 355.3 kilograms is "Three hundred fifty-five point three kilograms."In word form, numbers are expressed using words, making it easier to understand and communicate quantities. Here's a breakdown of the conversion:"Three hundred" represents the hundreds place value, which is 300."Fifty" represents the tens place value, which is 50."Five" represents the ones place value, which is 5."Point" indicates the decimal point."Three" represents the tenths place value, which is 3."Kilograms" specifies the unit of measurement.So, when you combine these components, you get "Three hundred fifty-five point three kilograms." This accurately describes the quantity of 355.3 kilograms in word form, emphasizing the hundreds, tens, ones, tenths, and the unit of measurement. This notation is especially important in contexts where precise measurement and clear communication of quantities are necessary, such as in scientific, industrial, or trade-related scenarios.For more questions on kilograms -
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what is true about a number with base A and exponent B?
Answer:
A^B = A*A*A*... (B number of times)
In the right triangle shown, m\angle A=45\degreem∠A=45°m, angle, A, equals, 45, degree and AB = 12AB=12A, B, equals, 12. How long is BC
Answer:
[tex]BC=6\sqrt{2}\ units[/tex]
Step-by-step explanation:
In this problem i will assume that the side AB is the hypotenuse
The picture in the attached figure
we know that
In a right triangle, if one angle is 45 degrees, then the other angle complementary is equal to 45 degrees too
so
[tex]m\angle B=45^o[/tex]
In the right triangle ABC
[tex]cos(B)=\frac{BC}{AB}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
we have
[tex]cos(45^o)=\frac{\sqrt{2}}{2}[/tex]
[tex]AB=12\ units[/tex]
substitute
[tex]BC=cos(B)(AB)[/tex]
[tex]BC=\frac{\sqrt{2}}{2}(12)=6\sqrt{2}\ units[/tex]
Answer: 6 square root 2
Step-by-step explanation:
Mrs.Mroc has 35 students in her science class.If her class increases to 42 students next
year, what will be the percent of change?
Answer:
20%
Step-by-step explanation:
Find the increase (subtract original number with final):
42-35= 7
Find the percent change (divide the increase by original number, then multiply by 100 to find the percentage):
[tex]\frac{7}{35}[/tex]*100=20
The percent change from 35 students to 42 students is 20%. This is calculated by using the formula for percent change: ((New Amount - Original Amount) / Original Amount) * 100.
Explanation:In this case, we are trying to calculate the percent change in the number of students in Mrs. Mroc's class. The formula for percent change is:
((New Amount - Original Amount) / Original Amount) * 100
The New Amount is 42 (the number of students next year), and the Original Amount is 35 (the current number of students). So the percent change would be (((42-35)/35)*100), which equals 20%.
So, if Mrs. Mroc's class increases from 35 students to 42 students next year, the percent change will be 20%.
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The null and alternative hypotheses for a test are given, as well as some information about the actual sample and the statistic that is computed for each randomization sample. Indicate where the randomization distribution will be centered. Hypotheses: H0:p=0.5 vs Ha:p>0.5 Sample: p^=0.7 , n=30 Randomization statistic =p^ Enter your answer in accordance to the question statement
Answer:
The randomization will be centered around 0.5
Step-by-step explanation:
n = 30
Null hypothesis, H₀ : p = 0.5
Alternative hypothesis, : p > 0.5
The randomization will be centered around 0.5
The indication of where the randomization distribution will be centered shows that the randomization distribution is always centered at the value of the parameter given in the null hypothesis, which is p = 0.5.
Where is the randomization distribution centered?The randomization distribution is centered on the value in the null hypothesis. Since the null hypothesis is given as H0:p=0.5 and the alternate hypothesis is Ha:p>0.5 with sample values of p^=0.7 and n=30, the value in the null hypothesis is used to center the randomization distribution.What is the randomization distribution?The randomization distribution is the graphical representation of data or all the values for the statistic in the form of a histogram based on the random assignment of the sample. The variability in a sample statistic results from the induced variability of the random sample.Thus, the randomization distribution is always centered at the value of the parameter given in the null hypothesis, which is p = 0.5.
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