Mr. Ledford is concerned about the amount of sleep the students in his district are getting. He selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the most recent grade-point average (GPA) for each student. His regression output along with a residual plot and a histogram of the residuals are given below.
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7
Required:
Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA?
Answers
Answer:
Hence, the data provides convincing evidence that a linear relationship exists between hours of sleep observed and academic performance as measured by GPA.
Step-by-step explanation:
Given the data:
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7
The scatter plot shows a positive linear trend. With the correlation Coefficient depicting a R value of 0.56. The residual plot also depicts a a randomly scattered values of the residual values. Similarly, a plot of the normal values of residuals
The data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have given data of the 14 seniors shown in the table.
To solve this question we will calculate the correlation coefficient 'r'
The formula for correlation coefficient :
[tex]\rm r =\frac{n\sum xy-\sum x \sum y}{\sqrt{[n\sum x^2-(\sum x)^2]}[n\sum y^2-(\sum y)^2]} }[/tex]
From the table the value of n = 14
[tex]\rm \sum x = 104.5[/tex] , [tex]\rm \sum y =47.7[/tex] , [tex]\rm \sum xy =357.8[/tex] , [tex]\rm \sum x^2 =797.25[/tex] , [tex]\rm \sum y^2 =163.09[/tex]
Put all the values in the above formula we get:
[tex]\rm r =\frac{14\times357.8-104.5 \times47.7}{\sqrt{[14\times 797.25-104.5^2][14\times163.09-47.7^2]} }[/tex]
[tex]\rm r = \frac{5009.2-4984.65}{\sqrt{(241.25)(7.97)} }[/tex]
[tex]\rm r = \frac{24.55}{43.849}[/tex]
r = 0.559 ≈ 0.56
The value of the correlation coefficient is 0.56 which is between the values 0.5 to 0.7 shows that the variables are moderately correlated.
Thus, the data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.
Learn more about the correlation here:
brainly.com/question/11705632
Related Questions
The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 4z^2+2z square meters. Factor this polynomial
Answers
Answer:
2z(2z+1)
Step-by-step explanation:
yup
4. What is the measure of each interior angle of
a regular 20-gon?
Answers
Answer:
162
Step-by-step explanation:
REALLY NEED HELP WITH THIS!!!
Answers
Answer:
9
Step-by-step explanation:
Solve the equation
Area =1/2(heightxbase)
27=1/2(Xx6)
54=6x
9 =x
please help me with this :D
Answers
|al-|b| + IcI. if a=-8;6=-5;c=1
Pls no links and only give answer if you know it
Answers
Answer:
4Step-by-step explanation:
Given
a = -8;b = -5;c = 1Absolute value is always positive:
|al - |b| + IcI = |-8l - |-5| + I1I =8 - 5 + 1 =4Find the average of f(x)=x^3-x over [0,2]
Answers
9514 1404 393
Answer:
1
Step-by-step explanation:
The average value of the function is the integral over the interval, divided by the width of the interval.
[tex]\displaystyle\overline{y}=\frac{1}{2-0}\int_0^2{f(x)}\,dx=\left.\frac{1}{2}\left(\frac{x^4}{4}-\frac{x^2}{2}\right)\right|_0^2=\frac{1}{2}\left(\frac{2^4}{4}-\frac{2^2}{2}\right)=\frac{4-2}{2}\\\\\boxed{\overline{y}=1}[/tex]
Suppose Tabitha finds an annuity that pays 7.0% annual interest, compounded semiannually. She decides to invest $650
semiannually in this annuity for 5 years. How much interest does she earn during the 5 years?
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer.
Answers
Answer:
Rounded to the nearest cent, over 5 years she will earn $ 916.89.
Step-by-step explanation:
Since Tabitha found an annuity that pays 7.0% annual interest, compounded semiannually, and she decided to invest $ 650 semiannually in this annuity for 5 years, to determine how much interest she will earn during the 5 years the following calculation must be performed:
650 x (1 + 0.07 / 2) ^ 5x2 = X
650 x (1 + 0.035) ^ 10 = X
650 x 1,035 ^ 10 = X
916,889 = X
Thus, rounded to the nearest cent, over 5 years she will earn $ 916.89.
Answer: 1125.41
Step-by-step explanation:
First, let’s find out how much is in the account after 5 years. We will use the savings annuity formula
A(t)=d((1+r/n)n⋅t−1)r/n
to find the value of A(5). We know that r=0.07, d=$650, n=2 compounding periods per year and, t=5 years. Substitute these values into the formula.
A(5)=$650 ((1+0.07/2)5⋅2−1)/(0.07/2)
Simplifying gives
A(5)=$650 ((1.035)10−1)/(0.035),
thus
A(5)=$7,625.41.
The sum of all deposits D5 is given by 5⋅2⋅$650=$6,500. Now, substitute these numbers into
A(5)=D5+I5
and solve for I5. This gives
$7,625.41=$6,500+I5,
yielding the total interest paid as $1,125.41. Enter 1125.41 as the answer.
What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)? 3 6 112 121
Answers
Answer:
121
Step-by-step explanation:121 ! just got it right.
Answer:
D)
Step-by-step explanation:
on edge
Cindy works on the weekends at the local coffee shop. Last Saturday she worked 7.5 hours and
on Sunday she worked 8 hours. She earns $9 per hour. How much did she earn last weekend?
F:97.00 G:89.50 H:139.50 J:109.00
Answers
Answer: H. 139.50
Step-by-step explanation:
Multiply 9 by 8 first and you get 72. Then multiply 9 by 7.5 and you get 67.5 then add 72 and 67.5 and you get 139.5 or 139.50
The equation of a circle is given as x2+ax+y2+by=c where a, b, and c are constants. The radius of the circle is given by the expression
(a2)2+(b2)2+c
a+b+c
(a2)2+(b2)2
c√
Answers
Answering actually A
Step-by-step explanation:
What is 15.74 rounded to the nearest whole number?( no links or files plz will get a brainliest)
Answers
Answer:
16
Step-by-step explanation:
Edit: Lol I learned this a while ago but imagine a ladder 5 or more goes up for sure 4 or less let it rest. Meaning anything over 5 goes up to the next digit and anything lower like 4 stays on that number
Answer:
16.
15.74 is closer to 16 than 15
A school district is considering moving the start of the school day at Groveland High from 8:00 a.m. to 9:00 a.m. to allow students to get more sleep at night. They want to estimate how many more hours of sleep teens get if their school starts at 9:00 a.m. compared to teens whose schools start at 8:00 a.m. The district takes random samples of 50 of students from Groveland High and 39 students from Phillips High School, which starts at 9:00 a.m., and surveys them about their sleep habits. The sample mean number of hours of sleep per student at Groveland is 7.1 hours, and the standard deviation is 1.7 hours. At Phillips, the sample mean is 8.3 hours of sleep, with a standard deviation of 1.9 hours. What is the 90% confidence interval for the difference in mean hours of sleep for students at the two high schools
Answers
Answer:
The answer is "[tex]\bold{(7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} }\\\\[/tex]"
Step-by-step explanation:
Given values:
[tex]\bar{x_1}=7.1\\\\\bar{x_2}=8.3\\\\s_1=1.7\\\\s_2=1.9\\\\n_1=50\\\\n_2=39[/tex]
Using formula:
[tex]\to (\bar{x_1} -\bar{x_2}) \pm t \sqrt{\frac{(s_1)^2}{n_1}+\frac{(s_1)^2}{n_2}} \\\\[/tex]
Put the values in the above formula:
[tex]\to (7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} \\\\[/tex]
Find the zeros of ƒ(x) = (x + 2)(x – 1)(x – 3)(x + 1).
Answers
Answer:
X=-2 x=1 x=3 and x=-1
Step-by-step explanation:
When the problem asks you to find the zeros all they are asking for is the solution so to solve all you need to do is set each individual piece equal to zero.
Here it is sry and thx!
Answers
Answer:
B
Step-by-step explanation:
hard to explain xD
Answer:
#2
Step-by-step explanation:
1x60+45=105
2x60+45=165
3x60+45=225
4x60+45=285
Please help! And don't give me a link, I know it's a scam.
Is a triangle with these measures possible?
52°, 18°, and 110°
Answers
Answer:
Yes.
Step-by-step explanation:
Well if the sum of the angles is equal to 180, then it's a triangle. Since [tex]52+18+110=180[/tex], a triangle with the measures 52°, 18°, and 110° is possible. Hope this helps!
example of a 400 word essay which choosing a college
Answers
Try starting with a question.
Begin with a bold statement.
Use an interesting quote.
Put the reader in medias res, that is, in the middle of things. ...
Challenge the reader by speaking directly to him/her.
Tell the reader what you do NOT want to do in your writing.
A box of 3 picture hangers sells for $2.22. What is the unit rate
Answers
Answer:
0.74 cents each unit piece
Step-by-step explanation:
2.22 ÷ 3 = 0.74
Look at the diagram.
What type of angle is angle B?
What type of angle is angle D?
Answers
Answer:
B - obtuse
D - acute
Step-by-step explanation:
Answer:
I think angle B is an obtuse angle and D is an acute angle. I'm not sure.
Hope this helps :)
PLEASE HELP 100 points I’m on a time(there’s a picture) With respect to air safety, in which year between 1966 and 1976 did the lowest number of air fatalities occur, and how
many passengers were killed in that year?
Year:1976,1974,1975
Passengers killed: 552,441,386
Answers
Looking at the column for number of passengers killed.
The lowest year was 1975 with 441 killed.
Answer:
1975
441
Step-by-step explanation:
simplify - root (9+y)^2 if y <-10
Answers
Answer:
− √ ( 9 + y ) 2 > 1
Explanation:
− √ ( 9 + y ) 2 , where y < − 10
Simplify the expression,
− √ ( 9 + y ) 2 = − ( 9 + y ) = − 9 − y
When y < − 10 , − y > 10
Subtract 9 from both sides,
− 9 − y > 1 Hence,
− √ ( 9 + y ) 2 > 1
The value of the expression -√(9 + y)² is -9 which is more than -10. So, it is incorrect.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ -√(9 + y)²
Simplify the expression, then we have
-√(9 + y)² = 0
(9 + y) = 0
9 + y = 0
y = - 9
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
What is the mean absolute deviation of the data set?
{12, 17, 12, 8,6)
Answers
Answer:The mean absolute deviation of the set of data is
2.24
.
Step-by-step explanation:
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answers
Answer:
90 degrees c
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Also can you give me brainlist???
Answer:
90 degrees celsius
Suppose you add two linear equations that form a system, and you get the result y = −2. How many solutions does the system have?
Answers
Answer:
This system will have 1 solution
Step-by-step explanation:
A linear system that has exactly one solution is called a consistent independent system. Consistent means that the lines intersect and independent means that the lines are distinct. Linear systems composed of lines that have the same slope and the y-intercept are said to be consistent dependent systems.
the three cubes shown weigh 12 ounces how many pounds would 24 cubes weigh A. 4.5 lb B. 6lb C. 18lb D. 72lb
Answers
holt mcdougal chapter 7 online answer key
Answers
Answer:
saan po yung pic hindi kopo maindihan
Choose all lengths that are equal to
6 feet 12 inches.
Answers
Answer:
Can you show a picture? Or like tell us the options?
Pls help 15 points What is the are of the trapezoid?
Answers
Answer:
D) 156 mm²
Step-by-step explanation:
18+8=26
26/2=13
13x12=156
Will give brainliest
Find the area of the following
parallelogram:
2 cm
4 cm
3 cm
A= [?] cm?
Answers
Answer:
Area of the parallelogram =base×height
area of parallelogram =3cm×2cm
area of parallelogram = 6cm²
The area of parallelogram is 6 square units.
What is a parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
For the given situation,
The base of the parallelogram,b = 3 cm
The height of the parallelogram,h = 2 cm
The formula of area of parallelogram is
[tex]A=bh[/tex]
⇒ [tex]A=(3)(2)[/tex]
⇒ [tex]A=6[/tex]
Hence we can conclude that the area of parallelogram is 6 square units.
Learn more about parallelogram here
https://brainly.com/question/16056863
#SPJ2
I BEG FOR MY LIFE EZ PLS
{{{{{{{PICTURE PROVIDED}}}}}}}}}
Answers
Answer:
Step-by-step explanation:
Answer:
B and D
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the base, height and depth. So, to find the correct answer, multiply each and see which are equal to 72:
A) 7*3*5 = 105
B) 8*9*1 = 72
C) 3*8*4 = 96
D) 12*3*2 = 72
E) 3*4*5 = 60
Since B and D are the only ones that equal 72, they are the possible answers to give a volume of 72 units cubed.
What’s 2/4 plus 3/8??
Mark brainliest!!!
No links!!
Answers
Step-by-step explanation:
[tex] \frac{2}{4} + \frac{3}{8} = \\ = \frac{4 + 3}{8} = \\ = \frac{7}{8} [/tex]
Answer:
The answer is 0.875 in decimal form but is 7/8 in fraction form
Step-by-step explanation: