Using the non-linear shooting method, the approximate solution for the given boundary-value problem y" = -yy' + y³, where 1.5 ≤ x ≤ 2, y(1) = 1/2, and y(2) = 1/3, is y(x) ≈ 1.1823, compared to the actual solution y(x) = 1/(x + 1) ≈ 0.4 for 1.5 ≤ x ≤ 2.
The non-linear shooting method is given below:
Given boundary-value problem: y" = -yy' + y³, where 1.5 ≤ x ≤ 2, y(1) = 1/2, and y(2) = 1/3.
We will use the non-linear shooting method with an accuracy of 10⁻¹.
Step 1: Guess an initial value for y'(1). Let's start with y'(1) = 1
Step 2: Solve the initial-value problem numerically using the guessed initial condition and a step size of h = 0.5. We will use a numerical method like Euler's method.
For each step, use the equations:
y[i+1] = y[i] + h * y'[i]
y'[i+1] = y'[i] + h * (-y[i] * y'[i] + y[i]³)
Iterating from x = 1 to x = 2 with a step size of h = 0.5:
Iteration 1:
x = 1, y = 1/2, y' = 1
x = 1.5, y = 1/2 + 0.5 * 1 = 1
x = 2, y = 1 + 0.5 * (-1 * 1 + 1³) = 1.25
Iteration 2:
Adjust the initial guess for y'(1) based on the error:
New guess for y'(1) = 1.5
Solve the initial-value problem again with the new guess:
x = 1, y = 1/2, y' = 1.5
x = 1.5, y = 1/2 + 0.5 * 1.5 = 1.25
x = 2, y = 1.25 + 0.5 * (-1.25 * 1.5 + 1.25³) = 1.1823
The approximate solution for the given boundary-value problem using the non-linear shooting method is y(x) ≈ 1.1823 for 1.5 ≤ x ≤ 2.
To compare with the actual solution y(x) = 1/(x + 1):
For x = 1.5, y = 1/(1.5 + 1) = 1/2.5 ≈ 0.4
For x = 2, y = 1/(2 + 1) = 1/3 ≈ 0.333
The actual solution is y(x) ≈ 0.4 for 1.5 ≤ x ≤ 2.
By comparing the approximate solution and the actual solution, we can assess the accuracy of the numerical method.
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me needs a hug and help
Answer: C
Step-by-step explanation:
Here is a graph of a quadratic function f(x). What is the minimum value (y-value only) of f(x)?
Answer:
Zero.
Step-by-step explanation:
The minimum value is where the function touches the x axis , at y = 0.
Use the Chain Rule to find dw/dt.
w = ln
sqrt2a.gif x2 + y2 + z2
, x = 4 sin t, y = 7 cos t, z = 9 tan t
Using the Chain Rule to dw/dt. w = ln [tex]\sqrt{2a}.gifx^{2} + y^{2} + z^{2}[/tex], x = 4 sin t, y = 7 cos t, z = 9 tan t the expression will give us the final result for dw/dt.
To find dw/dt using the Chain Rule,
we'll start by expressing w as a composition of functions and then differentiate it step by step.
Given:
w = ln[tex](\sqrt{} (x^2 + y^2 + z^2))[/tex], where x = 4 sin(t), y = 7 cos(t), and z = 9 tan(t).
We'll first substitute the values of x, y, and z into the expression for w:
w = ln[tex](\sqrt{} ((4 sin(t))^2[/tex] + [tex](7 cos(t))^2[/tex] + [tex](9 tan(t))^2))[/tex]
Next, we'll differentiate w with respect to t using the Chain Rule.
The Chain Rule states that if we have a composite function f(g(t)),
its derivative is given by f'(g(t)) ×g'(t).
In our case, f(u) = ln[tex](\sqrt{u}[/tex] and g(t) represents the expressions within the square root.
Applying the Chain Rule, we have:
dw/dt = [tex](1/\sqrt{} (x^2 + y^2 + z^2))[/tex] × (2xdx/dt + 2ydy/dt + 2z×dz/dt)
Substituting the expressions for x, y, and z, we get:
dw/dt = (1/[tex]\sqrt{} ((4 sin(t))^2 + (7 cos(t))^2[/tex]+[tex](9 tan(t))^2))[/tex] ×(2(4 sin(t))(cos(t)) + 2(7 cos(t))(-sin(t)) + [tex]2(9 tan(t))(sec^2(t)))[/tex]
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Can anyone pls help
Answer:
50
Step-by-step explanation:
if im thinking right
im SOO sorrYYy if its wrong
A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
less than 4 hours
4-8 hours
8-12 hours
more than 12 hours
above below
6
15
9
13
17
17
11
20
How many total students who spend more than 12 hours a week on screens were
surveyed?
The correct answer is that 13 students who spend more than 12 hours a week on screens were surveyed.
The provided data represents the number of students based on their screen time and whether their grade average is above or below 80.
To find the total number of students who spend more than 12 hours a week on screens, we need to look at the "Screen Time" category that corresponds to "more than 12 hours" and sum up the corresponding counts.
Looking at the data:
Screen Time:
less than 4 hours: 6 students
4-8 hours: 15 students
8-12 hours: 9 students
more than 12 hours: 13 students
If we consider only the "more than 12 hours" category, we find that there were 13 students.
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Does anyone know this one?
Answer:
-3
Step-by-step explanation:
(-5) - (-2) = (-3)
hope it helps
Answer:
there is a three degree difference between san Diego and Los Angeles
Fill in the blank. -6_-1*
>
<
=
Answer:
<
Step-by-step explanation:
-6 is lower than -1. you can make a little line and count backwards from 0. -1 is closer to 0 than -6 is, therefore -1 being bigger and the sign being <
help asap please i need to get thru this
Answer:
The Scale Factor is 1/4.
Step-by-step explanation:
if you multiply each side (of figure A) by 1/4, the product matches with figure B's corresponding sides. for example, 56 to 14, 28 to 7, and 64 to 16.
the scale factor is just how much a chosen shape is multiplied by to get the next shape.
to get bigger shapes into a smaller shape, multiply the sides by fractions like we did this problem.
A cylindrical soup can has a radius of 1.9 in. and is 5.9 in. tall. Find the volume of the can.
Answer:
66.93 in^3
Step-by-step explanation:
Volume = πr^2h
=> V = 22/7*(1.9)^2*5.9 = 66.93 in^3
The dot plots below show the test scores of some mathematics students and some science students:
Based on visual inspection of the dot plots, which group of students appears to have the larger average score?
The mathematics students
The science students
Both groups are similar.
Not enough information is available to draw a conclusion.
Answer:
Science students
Step-by-step explanation:
The width of a rectangular shed is 8 feet, and its length is 14 feet. Three of these expressions equal the perimeter of the garden, in feet. Which expression does NOT?
Answer:
That one
Step-by-step explanation:
It's kinda obvious if you look at the choices.
Answer:
8+14
Step-by-step explanation:
what fraction of an hour is 15 minutes pls help
Answer:
1/4 of an hour is 15 minutes
Step-by-step explanation:
Answer: 1/4 of an hr
Step-by-step explanation:
15/60 is 1/4
A hawk is flying 130 meters up in the sky and spots a rodent on the ground at a 20
degree angle of depression. To the nearest meter, what is the horizontal distance
between the hawk and the rodent?
Answer:
arc length d = ∫ √(1 + (dy/dx)²) dx
y = 228 - x²/57
dy/dx = -2x / 57
(dy/dx)² = (2x/57)²
Upper limit for integration:
y = 0 = 228 - x²/57
yields x = 114
d = ∫ √(1 + (2x/57)²) dx for 0 ≤ x ≤ 114 = 264.9 m
Step-by-step explanation:
The number of claims follows a negative binomial distribution with parameters β and r, where β is unknown and r is known. You wish to estimate β based on n observations, where xˉ is the mean of those observations. Determine the maximum likelihood estimate of β.
(a) xˉ/r2
(b) xˉ/r
(c) xˉ
(d) rxˉ
(e) r2xˉ
Since s = Σ(xi - x) / n is the sample variance therefore,
Option (a) x/r is correct.
To find the maximum likelihood estimate of β,
We need to maximize the likelihood function L(β) with respect to β.
The likelihood function for a negative binomial distribution with parameters β and r, given n observations with mean x, is,
⇒ L(β) = (Γ(r+n)/Γ(r)n!) (β^r / (β+x)^r+n) ∏([tex]x_i[/tex]+x)/(([tex]x_i[/tex]+β)^r+1
where Γ is the function and ∏ denotes the product over all n observations xi.
Taking the natural logarithm of the likelihood function, we get,
⇒ ln L(β) = ln(Γ(r+n)) - ln(Γ(r)) - ln(n!) + r ln(β) - (r+n) ln(β+x) + Σ ln(xi+x) - Σ ln(xi+β) - (r+1)Σ ln(xi+x)
To find the maximum likelihood estimate of β,
we take the derivative of ln L(β) with respect to β,
set it equal to zero, and solve for β,
⇒ d/dβ ln L(β) = r/β - (r+n)/(β+x) + Σ 1/(xi+β) - (r+1)Σ 1/(xi+x) = 0
We can solve this equation numerically using iterative methods, but we can also simplify it by using the fact that when the derivative of a function equals zero, the function is at a maximum or minimum.
Multiplying both sides of the equation by β(β+x), we get.
⇒ r(β+x) - (r+n)β + β(β+x)Σ 1/(xi+β) - (β+x)(r+1)Σ 1/(xi+x) = 0
Simplifying and solving for β, we get,
⇒ β = x(r+n-1) / (Σ 1/(xi+β) - (r+1)Σ 1/(xi+x))
We can use an iterative method to solve for β, starting with an initial estimate of β and updating it until convergence.
One common method is to use the Newton-Raphson algorithm.
After some algebraic manipulations,
we can show that the maximum likelihood estimate of β is,
⇒ B = x(r / s - 1)
Here s = Σ( - x) / n is the sample variance of the n observations. Therefore, the correct option is (a) x/r.
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In ABC Co. employees could bring n USB drives from home, install whatever they wanted including games, and otherwise modify their workstations. The consequence was that IT spent considerable time dealing with corrupted operating systems and had substantial expenses replacing machines. Rebuilding systems took "a lot of effort" according to an employee, and inevitably users had files in additional unexpected places, requiring manual efforts to retrieve those files. Users were down for a day or more. These incidents took time away from priority IT initiatives and required 3-24 hours each to identify the issue, mitigate and remediate. Educating users was helpful, but users still couldn’t manage themselves, particularly given increasingly sophisticated social engineering exploits. The Vice President of IT addressed several issues to improve the security of the infrastructure over the past five years, expanding on what was working, and changing what needed improvement. They virtualized 98% of the infrastructure, and still utilize custom-built applications where needed. According to an employee, "In the Windows environment we wanted to eliminate the havoc of allowing users admin rights. It makes me nervous from a security perspective, but it also inhibits productivity of both IT and end users."
They initially selected a product that had seemed simple in their trials, and it offered to fully automate deployment of software to local and remote employees via an intuitive web interface. It even offered remote access capabilities for remote employees. The results of a trial deployment, however, were much less than expected — important applications could not work without admin rights the way that product was designed. That’s when the IT department tested "PowerBroker" for Windows on his personal PC. "With "PowerBroker" for Windows I could navigate and discover assets, identify vulnerabilities, and most importantly lock down all applications to implement least privilege and remove all admin rights from users’ PCs," Romious discovered. And PowerBroker had flexibility in how it could be deployed and managed, which did take some time to decide, but in the end PowerBroker for Windows easily scaled to meet their enterprise needs and allow removal of admin rights from all Windows systems. PowerBroker has solved these challenges.
On an application-by-application basis, IT can then review the risk and vulnerabilities associated with the requested application by using the BeyondInsight platform included with PowerBroker for Windows. The BeyondInsight IT Risk Management Platform provides centralized reporting and analytics, giving visibility into the risks associated with assets that can be discovered and profiled. "BeyondInsight used with PowerBroker for Windows allows us to proactively assess and approve applications when warranted for business and when safe, rather than remediating after the havoc." The vulnerability scanner incorporated into PowerBroker for Windows and the BeyondInsight platform "has been invaluable" according to Romious. It ensures patches are applied, vulnerabilities are mitigated, and that nothing else becomes broken in the process. Fred Allen, VP of IT agrees, "The deployment of PowerBroker for Windows with BeyondInsight has gone well. It’s good to have a win-win after the challenges of the previous attempt to eliminate admin rights on users’ PCs.
Keeping in mind the IT security problem at ABC Co., what solution/s "PowerBroker" provided, from the perspective of the E-Commerce Security Environment you are aware of from ITMA 401 course?
What 3 vulnerable e-commerce points, which you studied of in ITMA 401 course, you also directly or indirectly encountered in this case study at ABC Co.?
What and how the 3 key technology concepts, of the Internet, got threatened at ABC Co.?
PowerBroker provided a solution to the security issue at ABC Co. by removing admin rights, improving application security, and addressing network security and data protection concerns.
From the perspective of the E-Commerce Security Environment, PowerBroker provided a solution to the issue of granting users administrative rights on their PCs, which posed security risks and productivity hindrances. By implementing PowerBroker for Windows, ABC Co. was able to remove admin rights from users' PCs and implement the principle of least privilege. This improved the security posture of the organization and reduced the likelihood of unauthorized access, data breaches, and system corruption.Three vulnerable e-commerce points encountered in this case study are:1. User Awareness and Education: Despite efforts to educate users about security risks, users at ABC Co. still struggled to manage their systems and fell victim to social engineering exploits. This highlights the ongoing challenge of ensuring user awareness and education to mitigate security risks.2. Application Security: The initial product deployed at ABC Co. failed to work without admin rights, indicating vulnerabilities in the design and implementation of the application. Application security is critical in the e-commerce environment to prevent unauthorized access, data breaches, and system compromise.3. Patch Management: The vulnerability scanner incorporated into PowerBroker for Windows and the BeyondInsight platform addressed the challenge of patch management. It ensured that patches were applied promptly, vulnerabilities were mitigated, and system integrity was maintained. Effective patch management is crucial to protect against known vulnerabilities and potential attacks.The three key technology concepts of the Internet that were threatened at ABC Co. include:1. Network Security: By allowing users to bring USB drives and make modifications to their workstations, ABC Co. faced risks of malware infections, unauthorized access, and compromised network security. The implementation of PowerBroker helped address these security concerns and enhance network security.2. Application Security: The challenges faced in finding an application deployment solution that worked without admin rights highlighted the importance of application security. PowerBroker provided a mechanism to lock down applications and implement least privilege, mitigating the risks associated with unauthorized access and malicious activities.3. Data Protection: The incidents at ABC Co., such as corrupted operating systems and unexpected file locations, demonstrated the need for robust data protection measures. By improving the security infrastructure and implementing PowerBroker, ABC Co. reduced the likelihood of data loss, unauthorized access, and data breaches.In summary, PowerBroker addressed the issue of granting admin rights, mitigated vulnerabilities in application security, and improved network security and data protection, thereby addressing key concerns within the E-Commerce Security Environment. The vulnerable e-commerce points included user awareness, application security, and patch management, while the threatened technology concepts were network security, application security, and data protection.For more questions on Power
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{A,B,C,D,E,F,G,H}
how many 4-element subsets are there in the set ?? and please
solve step by step
After considering the given data we conclude that the total number of 4-element subsets that can be generated is 70.
To evaluate the number of 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}, we can apply the combination formula:
[tex]nCr = n! / r!(n-r)![/tex]
Here,
n = maximum count of elements in the set
r = total count of elements we want to choose.
For the given case, n = 8 (since there are 8 elements in the set) and r = 4 (since we want to choose 4-element subsets).
Placing in these values, we get:
[tex]nCr = 8! / 4!(8-4)! = 8! / 4!4![/tex]
[tex]= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70[/tex]
Hence, creation of 70, 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}.
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a youth basketball has a diameter of about 8.75 inches. what is the volume of air, in cubic inches, that can fill the basketball? round your answer to the nearest hundredths place.
answer(s);
1.) 1,052.31 in^3
2.) 350.77 in^3
3.) 240.41 in^3
4.) 2,805.16 in^3
Answer:
this took hella long to do but it's B
What is the volume of a container with sides 1ft, 2ft, and 2.5 ft
Answer:
5ft^3
Step-by-step explanation:
The formula for volume is length × width × height.
so you multiply 1×2×2.5, which equals 5
Help please multiple choice interval. 20 Points. Thanks very much!
Answer:
D
Step-by-step explanation:
Two fifths of a number is 24.
what is the number?
Answer:
60
Step-by-step explanation:
half of 2/5 is 1/5 so half of 24 is 12.
since 12 is 1/5 of the number multiply 12 by 5 and you get 60.
The whole number will be 60 whose two fifths will be 24.
Given, Two fifths of a number is 24.
Writing in form of equation,
Let the whole number be x.
So, two fifth of x is 24.
[tex]\frac{2}{5} of x = 24[/tex]
[tex]\frac{2}{5} \times x = 24[/tex]
Apply cross multiplication,
[tex]x = \frac{24 \times 5}{2}[/tex]
x = 60.
Therefore the whole number is 60.
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help with this please
Answer:
a = 7. b = 24, c = 25. This is a Pythagorean triple
Step-by-step explanation:
PLSS HELP I WILL GIVE YOU BRAINLYEST!!
Students were surveyed about their
favorite sports to play in physed. The
results are represented in this arcle graph
If 48 students were surveyed, how many
chose soccer?
Part/total=%/100
A. 15
B. 12
C. 13
D. 10
Answer: C
So I was right, I guess.
How do I find degrees of monomials?
CAN SOMEONE HELP AND EXPLAIN WHAT TO DO PLEASEEEEEEEEEEEEEE
Answer:
a. 19 Questions
b. No, Collins grade was 81%, or B-minus :(
Step-by-step explanation:
There are 21 questions in total on the test. Collin wants a 90 percent at least. If you multiply 21 by 90 percent (as below), you will get 18.9
[tex]21 * .9\\=18.9[/tex]
Of course, you can't get 18.9 questions right (unless you're teacher gives .9 extra points lol, So we need to round UP to a whole number (don't round down because it'll give you a number lower than what 90 percent would equate to.
And, Collin got 17 questions right. That's equivalent to 81 percent of 21 (as below).
[tex]17 / 21\\=.8095[/tex]
This rounds to about 81%, meaning Collin did not reach his goal :(. Oh well, he'll just have to try harder next time!
Have a nice day, fam.
Use the method of undetermined coefficients to solve the initial value problem below. y'' + 7y=7 sin (√7t), y(0) = 8, y'(0)=√7 19 2 y =
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
To solve the initial value problem using the method of undetermined coefficients, we assume a particular solution of the form:
y_p(t) = A sin(√7t) + B cos(√7t)
where A and B are constants to be determined.
Taking the first and second derivatives of y_p(t), we have:
y'_p(t) = A√7 cos(√7t) - B√7 sin(√7t)
y''_p(t) = -A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)
Substituting these derivatives back into the differential equation, we get:
(-A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)) + 7(A sin(√7t) + B cos(√7t)) = 7 sin(√7t)
Simplifying, we have:
(-A(√7)^2 + 7A) sin(√7t) + (-B(√7)^2 + 7B) cos(√7t) = 7 sin(√7t)
To satisfy this equation for all t, the coefficients of sin(√7t) and cos(√7t) must be equal to the corresponding coefficients on the right side.
Therefore, we have the following system of equations:
-A(√7)^2 + 7A = 0 (coefficient of sin(√7t))
-B(√7)^2 + 7B = 7 (coefficient of cos(√7t))
Solving these equations, we find:
A = 0
B = 1
So, the particular solution is:
y_p(t) = cos(√7t)
To find the general solution, we need to find the complementary solution by solving the homogeneous equation:
y'' + 7y = 0
The characteristic equation is:
r^2 + 7 = 0
Solving this quadratic equation, we find two complex roots:
r₁ = √7i
r₂ = -√7i
The complementary solution is then:
y_c(t) = C₁ cos(√7t) + C₂ sin(√7t)
where C₁ and C₂ are constants to be determined.
Using the initial conditions y(0) = 8 and y'(0) = √7, we can substitute these values into the general solution and solve for C₁ and C₂.
y(0) = C₁ cos(0) + C₂ sin(0) = C₁ = 8
y'(0) = -C₁√7 sin(0) + C₂√7 cos(0) = C₂√7 = √7
Therefore, C₁ = 8 and C₂ = 1.
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
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Convert 13,000,000,000,000,000,000,000,000 to scientific notation.
Answer:
1.3 times 10 to the 25th power
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
Hi! The answer to your question is 1.3 x [tex]10^{25}[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Which of the following answers matches “The quotient of 9 and the sum of the quantities 5 and product of 8 and x.”
Answer:
I believe this is the answer 9/(5 + 8x)
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answer:
it does not form a triangle
Step-by-step explanation:
brainliest give me pls pls pls
Answer:
It forms a obtuse triangle
Step-by-step explanation:
Because two sides are the same.
can anyone expand and simply this for me (3x +2)(2x-5) ?
Answer: 5x-3
Step-by-step explanation:
3x+ 2x +2-5
5x -3
The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
(a) Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.
b)The value of chi-square statistic for the sample is 16.042, given that
(a)Chi-square test
The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.
Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.
Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)
Expected frequencies:To compute the expected frequencies of the data we use the formula:
Eij = (row total i * column total j) / n where
i is the row number and j is the column number.
To find the value of chi-square statistic, the following table is necessary:
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
We obtain the expected frequencies by the above formula, and these are listed in the table below.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519
The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.
Here, we have four rows and three columns.
Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.
Since we have four rows and three columns, the number of degrees of freedom will be 6.
Using the chi-square distribution table, the critical value is 12.592.
Since 16.04 > 12.592,
we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.
(b) Value of chi-square statisticThe formula to compute the chi-square statistic is
χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.
Calculating the chi-square statistic, we have
χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)
= 16.042 (rounded to three decimal places).
The value of chi-square statistic for the sample is 16.042.
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