At a plant that manufactures bars of steel, a machine is used to cut the bars to specific lengths. The machine has a dial that sets the length of the bars to be cut. However, the dial is currently out of alignment and the plant manager is collecting data to assess the situation. The following table shows 8 trials at different dial settings along with the actual output length of the bars that were cut. All measurements are in millimeters.
(a) Use the following grid to construct a scatterplot in which dial setting is the explanatory variable and output length is the response variable. Based on your graph, does a linear model seem appropriate? Justify your answer.
(b) Use the data to construct a least-squares regression line to predict output length from dial setting.
(c) Assume that all conditions for inference are met. Indicate the hypotheses appropriate to test whether there is a linear relationship between output length and dial setting
(d) The test statistic for the appropriate test is t=9.018. Do the data provide convincing statistical evidence that there is a linear relationship between output length and dial setting?
Answers
Check Attached Photos. Sorry, it didn't let me submit it through text because of "inappropriate language," despite me not having any in my answer.
For the plant which manufactures bars of steel, the conclusions are as follows;
A. The scatter graph is shown.
B. The equation is y = 2.204 + 1.007x
C. Null hypotheses (H₀); β = 0
Alternative hypotheses (Hₐ); β ≠ 0
D. P-value (0.0001) is less than the significance level (α = 0.05).
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
At a plant that manufactures bars of steel, a machine is used to cut the bars to specific lengths.
The machine has a dial that sets the length of the bars to be cut.
The dial is currently out of alignment and the plant manager is collecting data to assess the situation.
The following table shows 8 trials at different dial settings along with the actual output length of the bars that were cut.
All measurements are in millimeters.
Dail setting Output length
75 78
77 79
79 82
80 83
81 85
82 83
83 86
85 88
A. The scatter plot is shown below.
Based on the scatter plot, a linear model seems appropriate to the model relationships between the dial setting of the machine and the output length of the steel bar.
The scatter plot shows the strong (r = 0.965), positive, linear association. There do not appear to be any outliners.
B. From the data to construct a least-squares regression line to predict output length from dial setting. Then
y = (a + bx)
Let x be the dial setting machine and y be the output length of steel bars (in mm).
y = 2.204 + 1.007 x
C. All conditions for inference are met. Indicate the hypotheses appropriate to test whether there is a linear relationship between output length and dial setting.
Let β be the true slope of the population regression line relating the dial setting of the machine (x) and the output length of the steel bars (y) at the manufacturing plant.
Null hypotheses (H₀) ; β = 0
Alternative hypotheses (Hₐ) ; β ≠ 0
Appropriate test = slope of regression line t-test.
D. The test statistic for the appropriate test is t = 9.018 with 6 degrees of freedom (7 - 1)
The normal curve is shown;
Using calculator command t-CDF, with the alternative hypotheses as β≠0, then P-value = 0.0001.
In probability notation;
P(b≥0.017) = P(t≥9.018) = 0.00005
P-value = (2) × (0.00005) = 0.0001
P-value = 0.0001
Assume α = 0.05
Since our P-value (0.0001) is less than the significance level (α = 0.05), we do not convince statistical evidence that there is a linear relationship between output length and dial setting.
As the dial setting (x) increases, the output length of the steel bar (y) increases as well.
More about the null hypotheses and alternative hypotheses link is given below.
https://brainly.com/question/9504281
Related Questions
solve: log3(x)+log3(x-2)=log3(x+10)
Answers
log3 ( x ) + log3 ( x - 2 ) = log3 ( x + 10 )
log3 ( x )( x - 2 ) = log3( x + 10 )
log3 ( x^2 - 2x ) = log3( x + 10 )
x^2 - 2x = x + 10
x^2 - 3x - 10 = 0
( x - 5 )( x + 2 ) = 0 ==》x = 5 Or x = - 2
FIND THE AREA OF THE SHADED SECTION IN THE CIRCLE THE SHADED SECTION IS 35 DEGRESS AND THE RADIUS IS 5 INCHES. USE THE FORMULA: M/360 TIMES PIE R SQUARED
Answers
Answer:
Area of sector of circle = 7.6302 inches (Approx.)
Step-by-step explanation:
Given:
Angle of section = 35°
Radius of circle = 5 inch
Find:
Area of shaded section
Computation:
Area of shaded section = Area of sector of circle
Area of sector of circle = [θ/360][πr²]
Area of sector of circle = [35/360][(22/7)(5)²]
Area of sector of circle = [0.0972][(3.14)(25)]
Area of sector of circle = [0.0972][78.5]
Area of sector of circle = 7.6302 inches (Approx.)
459,450,441, find the 37th term
Answers
Answer:
135
Step-by-step explanation:
So, our first term is 459.
Lets find what our change in terms is. To do this, lets subtract the frist term by the second:
459-450
This will get you 9.
Now that we know our change per term, lets find our 37th term.
All we need to do, is take our first term, and subtract it by our change in terms times the amount of terms.(Note that we already know are 1st term, so we are multiplying the change in terms by 36, not 37. )
So this is what we can use to solve for this:
459-(9x37)
This equals
135.
Hope this helps!
Step-by-step explanation:
first term = a = 459
common difference = d = 450 - 459 = -9
nth term = an
n = -9
an = a + (n-1)d
= 459 +(37-1)-9
= 459 + (36)-9
= 459 -324
= 135
37 th term = 135
plz mark my answer as brainlist if you find it useful for you. hope this will be helpful to you .
Which diagram best represents the relationship among integers, rational numbers, and whole numbers?
Answers
Rational numbers, integers and whole numbers
2 / 7 - x = 5/4 what is the value of 'x'
Answers
Answer:
27/28
Step-by-step explanation:
2/7 - x =5/4
-2/7 -2/7
x=27/28
Carlos cut StartFraction 5 Over 12 EndFraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?
Answers
Answer:
Each piece of cloth is (1/12) of a yard long.
Step-by-step explanation:
Carlus cut 5/12 of a yard of cloth into 5 pieces of equal length.
To find the length of each piece of cloth, we need to find the quotient between the length of the piece of cloth, and the number of pieces in which we divide it.
This is:
length = [tex]\frac{(5/12)yd}{5} = \frac{5yd}{12*5} = \frac{1yd}{12} \frac{5}{5} = \frac{1 }{12} yd[/tex]
This means that the length of each piece of cloth is (1/12) of a yard long.
Answer:
1/12 trust,
because yes. >3
2022 / 2023
Micayla wants the print shop to reduce the size of her painting but keep the ratio of length to width so that it will fit her frame. Study the scale drawings to determine the proportional relationship between her painting and the frame she wants to use.
Answers
Answer:
The width of the frame must be 12 inches (15in by 12in)
Step-by-step explanation:
Given
See attachment for painting and frame
Required
Determine the dimension of the frame
To do this, we make use of the following scale ratio.
[tex]Scale = Length : Width[/tex]
For the painting,
[tex]Scale = 20: 16[/tex]
For the frame,
[tex]Scale = 15: w[/tex]
Since she wants to maintain the same ratio; both scale must be the same.
i.e.
[tex]15 : w = 20 : 16[/tex]
Express as fraction
[tex]\frac{w}{15} = \frac{16}{20}[/tex]
[tex]\frac{w}{15} = 0.8[/tex]
Make w the subject
[tex]w = 15 * 0.8[/tex]
[tex]w = 12[/tex]
The width of the frame must be 12 inches i.e. 15in by 12in frame
PLZZ HELP ME!!!
ANY LINKS WILL BE REPORTED
Find the volume of this object.
Answers
Answer:
24 will be your answer.
Step-by-step explanation:
0.8 k - 20 = -60
what does ‘k’ equal?
Answers
Answer:
K = -50
Step-by-step explanation:
0.8(-50) - 20 = -60, because 0.8(-50) = -40, and when you subtract a negative you would "add" those numbers. So it would be 40 + 20 = 60, which would make it -60.
Answer:
k equals -50Step-by-step explanation:
0.8 k - 20 = -60
0.8k = -60 + 20
0.8k = -0
k = [tex]\frac{-40}{0.8}[/tex]
k = -50
Please help I have been stuck for a while now
Answers
Answer:
B. Between x 2 and x 3
Step-by-step explanation:
Please Help! ~ Math ~ You will get +10 points! ~ Multiple Chouce ~ 1 Problem!
In a basketball game, Sarah scored 4 points more than twice the number of points Jamie scored. Jamie scored 3 ponts. How many points did Sarah score?
A. 1 Point
B. 7 Points
C. 10 Points
D. 12 Points-
Answers
Answer:
10
Step-by-step explanation:
If Jamie scored 3, and sarah scored twice that much, multiple 3 by two
3x2=6
Sarah also scored 4 more points then twice of his points.
6+4=10
Your answer is ten points
need by midnight pretty simple i just don't know how to explain it.
Answers
Answer:
Side x is adjacent to 30° angle.
Correct method is:
cos 30° = x/15 ⇒ x = 15*cos 30° ⇒ x = 12.99Diego is correct and Steven is wrong.
when finding sine consider the opposite side to the angle, not hypotenusewhen finding cosine consider adjacent side to the angle, not hypotenusepls I need help with this math question.
Answers
Answer: -4096
Step-by-step explanation:
Suppose you know that the prices paid for cars are normally distributed with a MEAN or $17,000 and a STANDARD DEVIATION of $500. Use the EMPIRICAL RULE to find the percentage of buyers who paid
Answers
Complete question :
Suppose you know that the prices paid for cars are normally distributed with a MEAN or $17,000 and a STANDARD DEVIATION of $500. Use the EMPIRICAL RULE to find the percentage of buyers who paid between 15500 and 17000
Answer:
49.85%
Step-by-step explanation:
Mean = 17000
Standard deviation = 500
Obtain the Z score, which is the number of standard deviations from the mean :
((17000 - 17000) / 500) = 0
((15500 - 17000) / 500) = - 3
-3 to 3 = (3 standard deviations)
However,
The value here is (-3 to 0) ; which is only 3 standard deviations to the left.
3 standard deviation = 99.7% (empirical rule)
Since it is only (-3 to 0) ; which is only 3 standard deviations to the left. ; the percentage will be halved
99.7% / 2 = 49.85%
Hence, percentage of buyers who paid between 15500 and 17000 is 49.85%
Guided Practice
Write an equation of the direct variation that includes the point (–8, 10).
A.
y= −4/5x
B.
y= 5/4x
C.
y= −5/4x
Answers
Answer:
C.
y= −5/4x
Step-by-step explanation:
Write an equation of the direct variation that includes the given point. (-8, 10)
1
first divide y by x to find the constant
2
Then write the equation using that constant. The constant can be written as a fraction or a decimal.
RESULT
Add 5 and 14, triple the sum, and then add four-
fifths.
Answers
Answer:
57.8 or 57 and four fifths
Step-by-step explanation:
5+14=19
19*3=57
57+0.8= 57.8
PLEASE HELP I don't understand this stuff yet. Brainliest give away!
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Answer: I think the answer is B
Step-by-step explanation: My reasoning is that since some houses are expensive, and some houses are very cheap, the average house is in the middle, and that is the median.
Answer:
c bc he should use the median cause it is in the affect the mean
Step-by-step explanation:
A butcher shop is selling steaks 2 for $7.00. The butcher sells 29 steaks today. How much money did the butcher make selling steaks today?
Answers
Answer:
The butcher made $101.50
Step-by-step explanation:
2 for 7.00
1 steak would be 7.00 divided by 2
7 divided by 2 is 3.5
1 steak is 3.50 dollars
29 steaks in total
29 multiplied by 3.50 is 101.5
Can someone please help i spendt 30 mins on this one question ?
Answers
Answer:
A
Step-by-step explanation:
To keep things short, use the distance formula to find the distance from each point from (0,0)
For the right triangle shown, whih equation can be used to find the vaule of x
Answers
Answer:
The answer is b
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
Write an equation in standard form for the line that passes through (4, 4) and has a x-intercept of 3?
PLEASE HELP AS SOON AS POSSIBLE 4/19/2021
Answers
Answer:
y=4(x-3)
Step-by-step explanation:
if x=3, subtract 3 from each side to get x-3=0
point (4, 4). That is, when x=4, y=4.
Plug those in and solve for a.
y=a(x-3)
4=a(4-3)
4=a(1)
4=a
Thus,
y=4(x-3)
A company that cleans carpets charges its customers a fixed amount for supplies plus an
additional amount per hour of cleaning. The graph models the linear relationship between the
total amount charged and the number of hours of cleaning.
Answers
Don’t quote me but, $15 per hour.
Explanation:
I just took the slope of the line,
(60 - 120) / (0 - 4)
-60 / -4
15
Castel and Chelsea are selling pies for a school fundraiser. Customers can buy cherry pies and lemon meringue pies. Castel sold 1 cherry pie and 5 lemon meringue pies for a total of $69. Chelsea sold 5 cherry pies and 7 lemon meringue pies for a total of $129. Find the cost each of one cherry pie and one lemon meringue pie.
Answers
Answer:
the cost each of one cherry pie and one lemon meringue pie is 9 and $12 respectively
Step-by-step explanation:
The computation of the cost of one cherry pie and the lemon meringue pie is shown below:
Let us assume the cherry pie be x
And, the lemon meringue pie be y
So according to the question
x + 5y = $69
5x + 7y = $129
Now multiply by 5 in the equation 1
5x + 25y = $345
5x + 7y = $129
18y = $216
y = $12
And, x would be
x + 5($12) = $69
x = $9
Hence, the cost each of one cherry pie and one lemon meringue pie is 9 and $12 respectively
please help
dgfhkcgfkgnglhgdh
Answers
Members of a soccer team raised $1416.50 to go to a tournament. They rented a bus
for $877.50 and budgeted $24.50 per player for meals. Determine the number of
players the team can bring to the tournament.
Answers
Answer: The answer is 22 players
Step-by-step explanation:
If y varies directly as z and inversely as x and y = –18 and z = 3 when x = 6, find y when x = 5 and z = –5.
36
18
9
64
Answers
Answer:
y = 36
Step-by-step explanation:
Given y varies directly as z and inversely as x then the equation relating them is
y = [tex]\frac{kz}{x}[/tex] ← k is the constant of variation
To find k use the condition y = - 18, z = 3 when x = 6 , then
- 18 = [tex]\frac{3k}{6}[/tex] ( multiply both sides by 6 )
- 108 = 3k ( divide both sides by 3 )
- 36 = k
y = [tex]\frac{-36z}{x}[/tex] ← equation of variation
When x = 5 and z = - 5, then
y = [tex]\frac{-36(-5)}{5}[/tex] = [tex]\frac{180}{5}[/tex] = 36
HELP ME PLEASE I'll give brainless.
Answers
POL= 59
Delta Math Help!!!
Triangle proofs help. I’ve gotten this far, but I have no idea what to do next!!
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The triangle ΔBAD is congruent to the triangle ΔCDA by SSS postulates.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
If the corresponding sides of the triangles are equal. Then the triangles will be a congruent triangles. And it is known as SSS postulates.
BD = AC and AB = CD
In triangles ΔBAD and ΔCDA, we have
BD = AC (Given)
AB = CD (Given)
AD = AD (Common side)
Then the triangle ΔBAD is compatible with the triangle ΔCDA by SSS proposes.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
Given the points A(4,6) and B(8, −2), what is the length of segment AB in units?
F √5
G 2√5
H 4√5
J 4
Answers
Answer:
Hi! The answer to your question is H. [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]Y1 = 6[/tex]
[tex]Y2 = -2[/tex]
[tex]X1 = 4[/tex]
[tex]X2 = 8[/tex]
[tex]AB = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]AB = \sqrt{(8-4)^2+(-2-6)^2}[/tex]
[tex]AB =\sqrt{(4)^2+(-8)^2}[/tex]
[tex]AB = \sqrt{16+64}[/tex]
[tex]AB = 4\sqrt{5}[/tex]
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☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Select all shapes that have a volume of 36pi cubic units. (see attached picture)
Answers
Answer:
a B and c because there the shape of the big triangles