A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per week; (2) several ten-minute exercise periods five days per week; and (3) several ten-minute periods five days per week using a home treadmill. The study report contains the following summary statistics about weight loss (in kilograms) after six months of treatment: Does the type of exercise treatments influence weight loss significantly? Use α = 5%. Treatment Mean Std. Dev. n Long periods 10.2 4.2 10 Multiple short periods 9.3 4.5 10 Multiple short periods with treadmill 10.2 5.2 10 The test statistic is:
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Answer:
Step-by-step explanation:
Hello!
For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:
Group 1: Single long exercise period five days per week
Group 2: Several 10' exercise periods five days per week
Group 3: Several 10' exercise periods five days per week using a home treadmill
All subjects were weighed before and after 6 months of training and their weight loss was determined.
The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.
To test this you have to conduct an ANOVA, with the hypothesis:
H₀: μ₁= μ₂= μ₃
H₁: At least one μi differs from the others. ∀ i=1, 2, 3
α: 0.05
The statistic is:
\(F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}\)
Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.
As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.
Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df
So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.
Treatments:
> The degrees of freedom between treatments are k-1 (k represents the number of treatments):
DfTr: 3-1= 2
>The sum of squares is:
SSTr: ∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= grand mean is the mean that results of all the groups together.
So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.
To calculate the grand mean you can sum the means of each group and dive it by the number of groups:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9
SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54
> The Means Squares is:
MSTr= SSTr/DFTr= 0.54/2= 0.27
Errors
>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.
DfEr= N-k= 30-3= 27
>The mean square error (MSEr) is the estimation of the variance error (σ\(_{e}^2\) → S\(_{e}^2\)), you have to use the following formula:
\(S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643\)
Finally you calculate the statistic:
\(F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012\)
This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:
\(F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35\)
Using the critical value approach, the decision rule is:
If \(F_{H_0}\) ≥ 3.35, reject the null hypothesis.
If \(F_{H_0}\) < 3.35, do not reject the null hypothesis.
The calculated value is less than the critical value, the decision is to not reject the null hypothesis.
So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"
I hope this helps!
Related Questions
-1000 2/3 is not real fraction. True or false
Answers
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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What is a Rational Number
A a problem that has =
B both positive and negative numbers
C Any number that can be written as a fraction
D A number that can tell the difference between right and wrong
Answers
-8 X-3x = -6 + 5 x
How to solve
Answers
Answer:
x = 7
Step-by-step explanation:
3x-5=x+9 (Adding 5 and -x to both signs of = Sign)
2x = 14
x = 7
help me pls no links
Answers
Answer:
this is a tough one but i know that sometimes it may seem hard but, with the right amount of practice, the hardest equations become the easiest to overcome. (Hint: Use PEMDAS)
Step-by-step explanation:
hope this helps you!
Answer:
I cant answer it i just need to talk to you its mya......
Step-by-step explanation:
The figure below is a net for a right rectangular prism.
11 m
13 m
11 m
7 m
11 m
11 m
What is the surface area of the right rectangular prism, in square meters?
Answers
The surface area of the right rectangular prism is given as follows:
358 m².
How to obtain the surface area?The surface area of a prism is obtained with the sum of the areas of each part of the prism.
The parts that compose the prism are given as follows:
Two rectangles of dimensions 7 ft and 12 ft.Two rectangles of dimensions 5 ft and 12 ft.Two rectangles of dimensions 5 ft and 7 ft.The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.
Hence the surface area of the prism is calculated as follows:
S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².
(multiplication by two due to the two rectangles with each of the dimensions).
Missing InformationThe prism is given by the image shown at the end of the answer.
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Kim has two babysitting offers for the same night. At the first job, she can babysit for 8 hours and
make $72. At the second job she can babysit for 6 hours and make $57. Which job pays more per
hour?
Answers
Answer:
The second job
Step-by-step explanation:
Divide 72 by 8 which equals 9
(72÷8=9)
Divide 57 by 6 which equals 9.5
(57÷6=9.5)
The job earns half more than than the first job in a hour
Add 7 by g then divide 10 by the result write an expression
Answers
Answer:
7 = 1 = 21
Step-by-step explanation:
Answer:
10 / (7 + g)
Step-by-step explanation:
Find the value of ab when a=4/7 and b= 4/11
Answers
Answer: 16/77
Step-by-step explanation: Here we're asked to evaluate ab
given that a = 4/7 and b = 4/11.
So we start by plugging in our given
values for a and b into the problem.
If we do this, ab would then be (4/7)(4/11).
When multiplying two fractions together, we multiply across
the numerator and we also multiply across the denominators.
So (4/7)(4/11) is 16/77 which is our final answer.
Answer:
16/77
Step-by-step explanation:
When two numbers are close togtether, you want to multiply them. Since it is ab, you multiply a and b.
a= 4/7
b= 4/11
so, 4/7 times 4/11
When you multiply fractions, you multiply the numerators (the top number of a fraction) of the fractions together. You also multiply the denominators(the bottom number) of the fractions together.
So, let's multiply the numerators first.
4 times 4 equals 16, so that is the new numerator
7 times 11 is 77, so that is the new denominator
Let's combine it into a fraction. Numerator/denominator= 16/77
Sometimes, you will need to reduce. Reducing meaning that you divide the fraction by a number so it can't be reduced/divided anymore. Until a fraction is at it's simplest form.
Example: 2/4 reduces to 1/2 because both the numerator, 2, and the denominator, 4, can be reduced by 2. As you can see, 1/2 is at it's simplest form and cannot be reduced any further.
Write (9 + 6i) − (1 + 3i) as a complex number in standard form.
Answers
Answer:
8 +3i
Step-by-step explanation:
(9 + 6i) − (1 + 3i)
Distribute the minus sign
(9 + 6i) − 1 - 3i
Combine like terms
9-1 + 6i -3i
8 +3i
Find the surface area
Answers
Answer: 120 yds
Step-by-step explanation:
48+30+24+18+120 yds
At a supermarket, there are 118 customers. If 45 have purchased shirts, 59 have
purchased pants, and 40 have purchased neither, how many purchased both shirts and
pants?
Answers
Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.
What is a Venn Diagram?A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.
In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.
The total number of customers at a supermarket = 118
The number of customers who purchased shirts, n(A) = 45
The number of customers who purchased pants, n(B) = 59
The number of customers who purchased neither shirts nor pants = 40
Let the number of customers who purchased both shirts and pants = n(A ∩ B)
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78
Substituting values:
78 = 45 + 59 - n(A ∩ B)
Solving for n(A ∩ B), we get:
n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26
Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.
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Annie borrowed $354 from her parents to buy a tablet. She plans to pay the money back in 2 equal payments per month for the next 12 months.
How much will each payment b
Answers
9514 1404 393
Answer:
$14.75
Step-by-step explanation:
Each of Annie's 24 payments will be ...
$354/24 = $14.75
Suppose that 650lb of coffee are sold when the price is $4 per pound
Answers
Money earned = $162.50
Explanation:
650 / 4 – You make $4 for every pound sold
= 162.5
Which is $162.50
graphing a function and its inverse
consider the graph of f(x)=x^2 and its inverse, f^-1 (x)=-^+ square root of X
Answers
Answer:
\(f^{-1}(x)=\sqrt{x}\)
Step-by-step explanation:
Check images below.
please help me babes i’m back at it again lol help
Answers
so first you want to make it so the two fraction coefficients have the same denominator
you would have to change -2/3 to -4/6
add the two like terms
-5/6e- 4/6e = -9/6e
solve for e
-9/6e = -24
-9e = -144
e = 16
hope this helped :)
How do u do 2 and 4 I’m really trying to get my grades up I’m failing 3 classes
Answers
PLEASE HELP ME I NEED HELP PLEASE HELP
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Answer:
1st question is 1:2
2nd question is 5
Step-by-step explanation:
15 times two is 30, so if you divide both 15 and 30 by 15, you get 1:2
Divide 300 and 60 and you get 5.
Answer:
1/2 5
Step-by-step explanation:
so the push ups you would divide 300 by 60 and the ratio is 1/2 because 15 plus 15 equals 30 so yea its 1/2
help pls. the question is in the picture at the top.
Answers
Answer:
solve for 6x+8
Answer:
x = 3
Step-by-step explanation:
Since ∠ P and ∠ S are congruent then the triangle is isosceles and
PT = TS , substitute values
7x + 4 = 5x + 10 ( subtract 5x from both sides )
2x + 4 = 10 ( subtract 4 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Question 4 of 10
Which situation best illustrates the concept of absolute advantage?
A. A German factory can build more sports cars than foreign factories.
B. Most of the world's largest companies have operations in many different countries.
C. The total value of Japanese imports is greater than the total value of the country's exports.
D. A French restaurant buys food from nearby farms to support the local economy.
Answers
Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.
Absolute advantage is the potential of an individual, a company, or a country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.
A factory in German has an absolute advantage because it can produce more sports car than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.
Therefore, the correct answer is option A.
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Approximately 78.9% of high school students in the United States have an iPhone. if a random sample of 50 students is selected what is the probability that less than 75% of the sample students have iPhones?
Answers
The probability that less than 75% of the sample students have iPhones is approximately 0.2478.
What is probability?
This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.
Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)
Using the binomial probability formula, we have:
P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37
However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.
Using the normal approximation, we can standardize the random variable X:
Z = (X - μ) / σ
where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.
Then, we have:
P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)
Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.
Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.
Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.
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Please help me solve this
Answers
BA=(3),(3),(-1) is the answer
A community would like to add a brick paver border around their swimming pool. They created the following image to represent the pool with the border. A large rectangle with a length of 48 feet and a width of 28 feet. Inside of it is another rectangle with a length of 32 feet and a width of 12 feet. Part A: Find the total area of the brick paver border that surrounds the 12 ft by 32 ft pool. Show your work. (2 points) Part B: If brick pavers cost $8 per square foot, what is the total cost of the brick pavers needed for this project? Explain. (2 points)
Answers
Part A: The total area of the brick paver border is \(960\) square feet.
Part B: The total cost of the brick pavers needed for this project is $\(7,680\).
Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.
The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.
Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).
Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).
Note: The calculations provided assume that the border consists of a single layer of brick pavers.
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in January the depth of a lake was 943 feet in August the depth of the lake was 754.4 what is the percentage decrease of the depth of the lake from January to August
Answers
The percentage decrease of the depth of the lake from January to August is 20%.
What is percentage decrease?The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.
Given,
The depth of lake in January = 943 feet
The depth of lake in August = 754.4 feet
The difference is = (943-754.4) feet
= 186.6 feet
So, the percentage decrease of the depth of the lake from January to August will be = (186.6 ÷ 943) × 100
= 20%
Therefore, the answer is 20%.
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If a = 4 units, b = 6 units, and c = 10 units, what is the volume of the three prisms above?
Answers
50.4 is 36% of what number?
Please explain step by step to get marked!
Answers
Answer:
36% of 140 = 50.4
Step-by-step explanation:
36% of what number = 50.4
... is equivalent to:
36% × ? = 50.4
36% × ? = 50.4 =>
? =
50.4 ÷ 36% =
50.4 ÷ (36 ÷ 100) =
(100 × 50.4) ÷ 36 =
5,040 ÷ 36 =
140
36% of 140 = 50.4
A bag contains colored tiles.
. 3 tiles are red
.6 tiles are green
. 3 tiles are blue
A lile will be randomly selected from the bag. What is the probability in decimal
form that the tile selected will be green?
Answers
Answer:
50%
Step-by-step explanation:
there are 12 total, half are green
The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?
Answers
The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
What is Polynomial function?
A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.
Given that;
The degree of the polynomial function f(x) is 3.
And, The roots of the equation f(x) = 0 are -1, 0, and 4.
Now, The polynomial function are calculated as;
f (x) = 0
(x + 1) (x - 0) (x - 4) = 0
x (x + 1) (x - 4) = 0
x (x² - 4x + x - 4) = 0
x (x² - 3x - 4) = 0
x³ - 3x² - 4x = 0
Thus, The polynomial function is;
x³ - 3x² - 4x = 0
Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.
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A college student takes the same number of credits each semester. They had 8 credits when they started, and after 5 semesters, they had 58 credits.
Which of these expresses the rate at which they is earning credits?
Answers
Answer:
There are 10 credits per semester.
Step-by-step explanation:
Given that: A college student takes the same number of credits each semester.
They had 8 credits when they started, and after 5 semesters, they had total 58 credits.
Now, In which rate they are earning credits per semester,
for that use the formula:
\(rate=\frac{change of credits}{total no of semeters}\)
rate=50/5
The change in credits is 58-8 = 50, since the
student earned 50 credits in 5 semesters.
So the rate at which they are earning credits per semester is:
Rate = 10 credits per semester.
Hence, there are 10 credits per semester.
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need this by today! Pls help! Im desperate! I will give correct anwser brainliest!
Answers
How the grinch stole Christmas- 25%
Rudolph the red nosed reindeer- 37.5%
Frosty the snowman- 6.25%
Adam is finding 10 less than 708 mentally. He thinks the tens digit and the hundreds digit will change. He gets 698 for his answer. Is Adam's thinking correct? Explain.
Answers
Answer:
Adam's thinking is not correct.
When subtracting 10 from 708, we need to borrow 1 from the hundreds digit and add it to the tens digit. This will result in a new hundreds digit of 6 and a new tens digit of 9. The ones digit remains the same. Therefore, the correct answer would be 698.
Adam's answer is also 698, but his reasoning is incorrect. He thinks that both the tens and hundreds digits change, which is not the case. In reality, only the tens digit changes while the hundreds digit decreases by 1 due to the borrowing process.
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