The following data were collected from a sample of fathers and sons. The heights are given in inches. Construct a 95% confidence interval for the slope of the regression line. Round your answers to two decimal places, if necessary.
Heights of Fathers and Sons (in Inches)
Height of Father, x: 65, 67, 66, 71, 65, 70, 73, 71, 69
Height of Son, y: 69, 67, 68, 73, 65, 73, 76, 73, 70
Answers
To construct a 95% confidence interval for the slope of the regression line, we can follow these steps:
Step 1: Calculate the necessary statistics:
- Compute the means of both the heights of fathers (x) and sons (y).
- Calculate the standard deviation of both x and y.
- Determine the correlation coefficient between x and y.
Using the provided data, we find the following statistics:
- Mean of x: (65 + 67 + 66 + 71 + 65 + 70 + 73 + 71 + 69) / 9 = 68.33
- Mean of y: (69 + 67 + 68 + 73 + 65 + 73 + 76 + 73 + 70) / 9 = 70.22
- Standard deviation of x: 2.56
- Standard deviation of y: 2.79
- Correlation coefficient (r): 0.752
Step 2: Calculate the standard error of the slope (SE):
- SE = (standard deviation of y) / (standard deviation of x) * (1 - r^2)^(1/2)
Plugging in the values:
- SE = (2.79) / (2.56) * (1 - 0.752^2)^(1/2) ≈ 0.378
Step 3: Determine the critical value for a 95% confidence interval. Since we are calculating the confidence interval for the slope, we need to refer to the t-distribution with n-2 degrees of freedom (where n is the number of data points, which is 9 in this case). For a 95% confidence interval, the critical value is approximately 2.31.
Step 4: Calculate the confidence interval:
- Slope ± (critical value * SE)
Plugging in the values:
- Slope ± (2.31 * 0.378)
The result will be the 95% confidence interval for the slope of the regression line.
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Related Questions
Can anyone help me please
Answers
In the line of symetry for this parabola is x = -1.
The maxima or minima of the parabola is \(-\frac{21}{4}\)
Estimate the gradient of the curve at x = 4 is 5.
The equation of the tangent of the point (4, 1) is 5x² - y² - 40x + 2y + 89 = 0.
The gradient of the curve at the point (-1, 1) is -1.
The steps are as follows:
The function of parabola y = x² - 3x - 3
(i) In the line of symetry for this parabola.
Symetry of the parabola:
x = \(-\frac{b}{2a}\) → for y = ax² + bx + c
x = \(-\frac{-3}{-3}\)
x = -1
(ii) The maxima or minima of the parabola.
The maximum or minimum parabola can be found when the derivative is 0
y = x² - 3x - 3
y' = 2x - 3
0 = 2x - 3
2x = 3
x = \(\frac{3}{2}\)
The maxima or minima of the parabola
y = x² - 3x - 3
= ( \(\frac{3}{2}\) )² - 3 ( \(\frac{3}{2}\) ) - 3
= \(\frac{9}{4}\) - \(\frac{9}{2}\) - 3
= \(\frac{9}{4}\) - \(\frac{18}{4}\) - \(\frac{12}{4}\)
= \(-\frac{21}{4}\)
(iii) Estimate the gradient of the curve at x = 4
y = x² - 3x - 3
y' = 2x - 3
y' = m = 2(4) - 3
= 8 - 3
= 5
y = x² - 3x - 3
y = 4² - 3(4) - 3
= 16 - 12 - 3
= 1
(iv) The equation of the tangent of the point (4, 1)
(y - b)² = m (x - a)²
(y - 1)² = 5 (x - 4)²
y² - 2y + 1 = 5 (x² - 8x + 16)
y² - 2y + 1 = 5x² - 40x + 90
5x² - y² - 40x + 2y + 90 - 1 = 0
5x² - y² - 40x + 2y + 89 = 0
(v) The gradient of the curve at the point (-1, 1)
y = x² - 3x - 3
y' = 2x - 3
y' = m = 2(1) - 3
= 2 - 3
= -1
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Suppose that Sin(θ)=5/13 and cos(θ)=-12/13. Find the value of tan(θ), cot (θ), CSC (θ), and sec (θ). Find the value of tan(2θ)
I know the values are tanθ=5/12, cscθ=13/5, secθ=13/-12 and cotθ=-12/5 but I don't know how to find tan(2θ)
Answers
Answer:
Because θ lies in quadrant II, 2θ must lie in quadrant IV. This means the tangent of 2θ is negative.
The adjacent side to θ is 7 because √(25²-24²)=7, so tanθ=7/24.
The double angle formula for tangent is tan 2θ = (2 tan θ) / (1 − tan² θ).
Substituting the value for tanθ in and keeping in mind that this is in quadrant IV, we get tan 2θ = -(2(7/24)/(1-(7/24)²)).
Simplified, this becomes tan 2θ = -336/527.
Therefore, the answer is C. -336/527.
Which of the following statements for a simple graph is correct?a) Every path is a trailb) Every trail is a pathc) Every trail is a path as well as every path is a traild) Path and trail have no relation
Answers
Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.
In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.
Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.
Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.
Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.
Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.
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Find the slope of the line passing through the points (-3,1) and (-8,5)
Answers
Answer:
-4/5
Step-by-step explanation:
y2-y1/x2-x1 is the formula for slope
If 48000 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent. (a) Annual: $____ (b) Semiannual: $_____ (c) Monthly $_____
(d) Daily $_____
Answers
To calculate the value of the investment, we can use the following formula:
FV = PV * (1 + r/n)^nt
FV = 48,000 * (1 + 0.09/365)^1825 = 66,593.99
As you can see, the more frequently the interest is compounded, the higher the future value of the investment. This is because the interest earned on the interest is reinvested, which results in even more interest being earned in the future. (a) The value of the investment at the end of 5 years, with annual compounding, is approximately $71,578.10. This is calculated using the formula A = P(1 + r/n)^(nt), where P is the principal amount of $48,000, r is the interest rate of 9% (0.09 as a decimal), n is 1 for annual compounding, and t is 5 years. Plugging these values into the formula, we find A = 48000(1 + 0.09/1)^(15) = $71,578.10. Investing $48,000 at an annual interest rate of 9% with annual compounding would yield approximately $71,578.10 after 5 years.
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The value of (1+tan2A)(1-sec A)(1+sec A) is
Answers
The value of (1+tan2A)(1-sec A)(1+sec A) is 1.
We can simplify the given expression using the trigonometric identities:
tan2A = 2tanA/(1-tan²A) and sec A = 1/cos A.
To simplify the given expression (1+tan²A)(1-secA)(1+secA), we can start by using trigonometric identities to express the terms in the expression in terms of a single trigonometric function.
Substituting these values, we get:
(1+tan2A)(1-sec A)(1+sec A)
= [1+2tanA/(1-tan²A)][1-1/cos A][1+1/cos A]
= [1-tan²A+2tanA][cos A-1/cos²A]
= [sec²A+2tanA][cos²A-1/cos²A]
= [sec²A+2tanA][sin²A/cos²A]
= [1/cos²A+2sinA/cosA][sin²A/cos²A]
= sin²A/cos²A
= 1
Therefore, the value of (1+tan2A)(1-sec A)(1+sec A) is 1.
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Given:
Prove:
Answer ASAP, please!:)
Answers
Answer:
Whats the question. I think I can help if there is a picture or if there are more words
Solve by elimination
Pls explain how you got your answer
8x - 6y = 84
4x-42=3y
Answers
The system of equations has infinite many solutions
How to solve the system of equationsFrom the question, we have the following parameters that can be used in our computation:
8x - 6y = 84
4x-42=3y
Rewrite as
8x - 6y = 84
4x- 3y = 42
Multiply the second by 2
8x - 6y = 84
8x - 6y = 84
Subtract the equations
0 = 0
The above means that the equation has infinite many solutions
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A number divided by 14
Answers
Answer:
it could be either 1, 2 or 7
Step-by-step explanation:
1×14=14
2×7=14
7×2=14
Please help! Pleaseeee! It’s not that hard
Answers
Answer:
B
Step-by-step explanation:
PLEASE HELP BRAINIEST ❤️
Answers
Explanation:
If y = (-10/6)x + 10 is the line in pic
And if the y-int move to 8 and keep using the same slope:
y = (-10/6)x + 8
If we were to draw we can see that we start at unit 8 then move 10 unit and move to the right 6 unit we can see that the line move down 2 unit.
△ABC has vertices at A(5, -1), B(1, -6), and C(3, -2). Brionna performs two transformations on her preimage. Firstly, she translates the triangle 7 units up and 2 units right. Secondly, she reflects the object across the line x=0. What are the coordinates of her image A’’, B’’, C’’? Use the coordinate plane provided to map Brionna’s transformations.
HELP PLSSS
Answers
Therefore, the coordinates of the image triangle △A''B''C'' are:
A''(-7, 0)
B''(-3, -4)
C''(-5, 0
What is angle?In geometry, an angle is the figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. The measure of an angle is typically given in degrees or radians, and represents the amount of rotation needed to rotate one of the sides of the angle around the vertex until it overlaps with the other side.
Angles are commonly used in various fields, including mathematics, physics, engineering, and architecture. They are also used in everyday life, such as measuring the angle between two walls to determine whether a piece of furniture will fit in a room, or measuring the angle between the hands of a clock to determine the time.
Firstly, let's find the coordinates of the image after the translation. We can achieve this by adding 7 to the y-coordinates of each point and adding 2 to the x-coordinates:
A'(7, 0): (5, -1) → (7+2, -1+7)
B'(3, -4): (1, -6) → (3+2, -6+7)
C'(5, -0): (3, -2) → (5+2, -2+7)
Next, let's find the coordinates of the image after reflecting across the line x=0. We can achieve this by changing the sign of the x-coordinates:
A''(-7, 0): (7, 0) → (-7, 0)
B''(-3, -4): (3, -4) → (-3, -4)
C''(-5, 0): (5, 0) → (-5, 0)
Therefore, the coordinates of the image triangle △A''B''C'' are:
A''(-7, 0)
B''(-3, -4)
C''(-5, 0)
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Last year, 140 people in a community had cell phones. This year, the number
of people in the community with cell phones has increased by 65%.
A. Wat is the percent of increase?
65%
B. What is the change in the number of people with cell phones?
C. How many people in the community have cell phones this year?
Answers
Answer:
Part B: 91 people
Step-by-step explanation:
Sorry i cant add a explanation, because im still learning about it.*EXTRA POINTS* Identify each pair of angles as-----
vertical, supplementary, corresponding, alternate interior, alternate exterior, or consecutive (same-side) interior:
Answers
2-alternative exterior
3-corresponding
1. Suppose you are taking a school bus that gets7 miles per gallon. If you will be driving 154 miles,how many gallons of gas will you need ?
Answers
22 gallons
1) In this question, we need to assume that the number of gallons of gas per mile is constant.
2) Thus, we can write out the following proportion:
\(\begin{gathered} 1-----7miles \\ g------154 \\ \frac{1}{g}=\frac{7}{154} \\ 7g=154 \\ \frac{7g}{7}=\frac{154}{7} \\ g=22 \end{gathered}\)So, we can state that I will need 22 gallons of gas to make 154 miles.
Simplify 2/4/8 what the awnser
Answers
Answer:
2 1/2
Step-by-step explanation:
10
13
16
19
22
25
28
What is the mean?
What is the standard deviation?
What percentage of values should fall between 19 and 22?
Which value has a score of -2?
Answers
Answer:
mean is 19
Step-by-step explanation:
sorry that's all I know
10+13+16+19+22+25+28=133
Now divide it by 7 since there are 7 numbers
133/7=19
What are the values of s and t?
Answers
Answer:
S=68
T=44
Step-by-step explanation:
G=E=68
F=180-(2×68):44
The slashes mean that the angles are the same. So the angle across from 68° is also 68°. Now we need to find the other one. We know a triangle = 180.
So add the two angles we have,
68 + 68 = 136
Now to find the angle subtract 180 from the sun of the two angles
180 - 136 = 44
The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table.
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
Answers
Answer:
(4,4)
Step-by-step explanation:
The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.
x^2 - 6x + 12 = 2x - 4
x^2 - 8x + 16 = 0
(x - 4)^2 = 0
x = 4
Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.
y = 2x - 4 = 2(4) - 4 = 4
Therefore, the solution of this system of equations is (4, 4).
Therefore, the correct answer is (4, 4).
So please help me with this!!
Answers
Answer:
The slope is undefined.
Hence, option C is true.
Step-by-step explanation:
The graph represents a vertical line.
We know that the slope of a vertical line is undefined.
Verification:
Taking two points
(0, -2)
(0, -4)
Finding the slope between (0, -2) and (0, -4)
slope = m = y₂-y₁ / x₂-x₁
= [(-4-(-2))] / [(0-0) ]
= [-4+2] / 0
= -2 / 0
= ∞
Thus, the slope is undefined.
Hence, option C is true.
Is y=3x^2+1 a linear or nonlinear equation?
Answers
Answer:
nonlinear
Step-by-step explanation:
because the axis is located below so its all gucci
Answer:
Nonlinear
Step-by-step explanation:
It's actually a parabola because it has a squared value.
Hope that helps and have a great day!
I nee someone to answer this and actually explain it to me please.
Answers
Given Data:
\(\begin{gathered} a=1.4 \\ b=-2.6 \\ c=5.2 \end{gathered}\)Here the point d is the horizontal distance, it can be found by adding the distance 'a' and 'c', since 'a' and 'c' are horizontal measurements. Th distance 'b' is given in vertical measurements. Thus, the distance 'b' can be ignored while finding the value of d.
\(\begin{gathered} d=a+c \\ d=1.4+5.2 \\ d=6.6 \end{gathered}\)Thus, the distant d is in 6.6 unit from the origin, or from the y-axis.
solve 3x-y=7 for x if weird answer will report
Answers
Answer:
x = 1/3y +7/3
Step-by-step explanation:
3x-y=7
Add y to each side
3x-y+y=7+y
3x = y+7
Divide each side by 3
3x/3 = y/3 + 7/3
x = 1/3y +7/3
Answer:
x= 7/3 + y/3
Step-by-step explanation:
divide each term by 3 and simplify
Amanda teaches all of the bass and viola students. All of her classes have the same number of students. Each class has the greatest possible number of students. How many of these classes does she teach? btw there is 20 bass students and 30 viola students.
Answers
Answer:
5 classes - 2 bass classes and 3 viola classes.
Step-by-step explanation:
Find the greatest common factor (GCF)
List the factors of 20 and 30:
20: 1, 2, 4, 5, 10, 20
30: 1, 2, 3, 5, 6, 10, 15, 30
The greatest factor that both numbers share is 10.
Therefore, there are 10 students in each class. So, she teaches 2 bass classes and 3 violas classes.
hope this helps! <3
The winner of an egg-eating contest ate 132 eggs in 11 minutes
What is the unit rate?
Answers
Answer:
12 eggs
Step-by-step explanation:
divide 132 by 11. hope this helped :)
Answer:
12 eggs per minute
Step-by-step explanation:
To find the unit rate, take the number of eggs and divide by the number of minutes
132eggs / 11 minutes
12 eggs per minute
5. A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long. The scale used for the drawing was 3 in.:5 ft. What are the height and length of the actual elephant?
Answers
Answer:
Length = 18ft Height = 10ft
Explaination:
We know that the height of the model is 6 inches, and we know that 3in=5ft. To find the height of the real thing we need to find out how many times 3 can fit into 6 which is 2 times. Multiply 2 by 5 to get 10, which is the height for the real elephant.
To find the length, we follow the same steps. First find out how many times 3 fits into 10.8, which is 3.6 times. Then multiply 3.6 by 5 to find the height which is 18ft.
hope this helps!
The height and length of the actual elephant are 10 ft high and 18 ft long.
How are scale drawings formed?For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
\(\rm 1\: ft : \dfrac{s}{k}\: in.\)
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
The scale used for the drawing was 3 in to 5 ft
We know that one basic unit in the drawing is in fact 3 inches.
These factors need to be multiplied with the base units of 5 ft for reality.
6 inches high
6 / 3 = 2
Now the elephant is 2 units high, which means in reality
2×5 = 10 ft high.
10.8 inches long
10.8 / 3 = 3.6
Therefore, the elephant is 3.6 units long, which means 3.6×5 = 18 ft long.
Hence the height and length of the actual elephant are 10 ft high and 18 ft long.
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M<7=100 find measure of <11
Answers
Answer:i think its 115 degres
Step-by-step explanation:
15 circles are cut-out of a rectangle with a length of 10 inches and a height of 6 inches. the circles are side by side. for a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. how much paper is wasted? (60 – 15π) square inches 15π square inches 45 square inches (60 – π) square inches
Answers
Answer:
\(60-15\pi\) square inches
Step-by-step explanation:
The area of the paper is \((6)(10)=60\) square inches.
The area of one circle is \(\pi(1^2)=\pi\). So, the combined area of the circles is \(15\pi\).
Taking the difference yields \(60-15\pi\).
Answer: its A
Step-by-step explanation:
edge 2023
Please help 100 points! MATHAMATICS
Answers
Congratulations dear user, All the answers given by you are absolutely correct!!
Create and solve the EQUATION. 4. The sum of seven times a number and 16 is 163.
Answers
An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.
The solution is 21.
How to determine the two unknown numbers?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;
7n + 16 = 163
7n = 163 - 16
7n = 147
n = 147/7
n = 21.
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