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
Find mZECD
E
D
C С
31°
A
B
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Type the correct answer in each box.
50°
60°
709
х
50°
The value of xis
°, and the value of y is
Answers
Answer:
x = 60°
y = 50°
Step-by-step explanation:
✔️x + 50° + 70° = 180° (sum of a triangle)
x + 120° = 180°
Subtract 120° from each side
x = 180° - 120°
x = 60°
✔️50° + 60° = x + y (exterior angle theorem of a triangle)
110° = x + y
Plug in the value of x
110° = 60° + y
Subtract 60° from each side
110° - 60° = y
50° = y
y = 50°
write an expression for the quotient of 9 and c
Answers
Answer:
[tex]\frac{9}{c}[/tex]
Step-by-step explanation:
i need your help on this question
Answers
Answer:
c, cause yeah
Answer:
C: a quadrilateral with exactly one pair of parallel sides
A consumer group surveyed the prices for white cotton extra-long twin sheet sets in five different department stores and reported the average price as $16 with standard deviation $3.81. Assume that the population is normal and has a standard deviation equal to $3.81. 9. Provide a 95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets. z* is 1.96
Answers
Answer:
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
(12.6604 ,19.3396)
Step-by-step explanation:
Step(i):-
Given that mean of the sample = 16
Given that the standard deviation of the sample = 3.81
The standard deviation of the Population = 3.81
Level of significance = 0.05
Step(ii):-
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
[tex](x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](16 - 1.96 (\frac{3.81)}{\sqrt{5} } , 16 +1.96 (\frac{3.81)}{\sqrt{5} })[/tex]
( 16 - 3.3396 , 16 + 3.3396)
(12.6604 ,19.3396)
Final answer:-
95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.
(12.6604 ,19.3396)
Where does the graph of cosine begin?
Answers
Answer:
Step-by-step explanation:
Cosine starts at 1 and then goes down till 180 degrees and then goes up again..
Hope this helps..
A restaurant noted what type of food its customers purchased last week.Here are the results
Answers
Answer:
There is no link to the results/question.
graphing sucks
ugh. but anyway does anybody know how to graph using only an equation? please explain thoroughly. PLEASE SAVE MY LIFE!
Answers
- you can substitue x and y for 1, or 0 and graph each point
- use desmos and copy it
- depending on the type of equation find the x-intercept, y-intercept, vertex and then draw a line between them
A car company is testing how well its cars handle skidding to a complete stop after hitting the brakes while going at different speeds on an asphalt road. The equation represents the car’s speed, in miles/hour, when the brakes are applied as a function of the distance, in feet, the car skids. The table of values represents the function S(D). Use the table of values to calculate the average rate of change between the given intervals. Then interpret what the average rate of change means in this context.
Answers
Answer:
D SD= sqrt(22.5D) Average Rate of Change
47 32.52
50 33.5 0.34
56 35.50 0.33
60 36.74 0.31
62 37.35 0.305
65 38.24 0.3
In the context of this problem, the average rate of change is the rate at which the car decelerates as it skids. As the distance that the car skids increases, the rate at which the car decelerates decreases at a gradual rate.
Step-by-step explanation:
I need help in this question. I am not understanding what it is telling me so HELP
Answers
Answer: You solve it its easy subtraction :)
Step-by-step explanation:
$14,000 - $5,358 - $2,834 - $4,132 = answer
An eyewitness observes a hit-and-run accident in New York City, where 95% of the cabs are yellow and 5% are blue. A police expert believes the witness is 80% reliable. That is, the witness will correctly identify the color of a cab 80% of the time. If the cab is actually yellow, there is an 80% chance the witness will assert it is yellow, and if the cab is actually blue, there is an 80% chance the witness will assert it is blue. If a witness asserts the cab was blue, what is the probability that the cab actually was blue
Answers
Answer:
0.1739 = 17.39% probability that the cab actually was blue
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Witness asserts the cab is blue.
Event B: The cab is blue.
Probability of a witness assessing that a cab is blue.
20% of 95%(yellow cab, witness assesses it is blue).
80% of 5%(blue cab, witness assesses it is blue). So
[tex]P(A) = 0.2*0.95 + 0.8*0.05 = 0.23[/tex]
Probability of being blue and the witness assessing that it is blue.
80% of 5%. So
[tex]P(A \cap B) = 0.8*0.05 = 0.04[/tex]
What is the probability that the cab actually was blue?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.04}{0.23} = 0.1739[/tex]
0.1739 = 17.39% probability that the cab actually was blue
how to graph an inequality y<1-2x
Answers
Answer:
Step-by-step explanation:
Tyson has two movie tickets and wants to randomly select one of six friends to go with him. He rolls a six-sided die to make his decision. He tested this model 60 times and recorded the results in this table.
Result of Roll Times Result Occurred
1 - 11
1 - 0.18
2 - 9
2 - 0.15
3 - 9
3 - 0.15
4 - 10
4 - 0.17
5 - 11
5 - 0.18
6 - 10
6 - 0.17
Do you think the relative frequency from the experiment is a good predictor of the theoretical probability? Why or why not?
Answers
Answer:
The relative frequency of rolling a particular number can be calculated using the formula
relative frequency , where f is the actual frequency of an event and n is the number of times the experiment is performed. This experiment had the following results:
The relative frequency of rolling a 1 is 0.2.
The relative frequency of rolling a 2 is about 0.23.
The relative frequency of rolling a 3 is about 0.13.
The relative frequency of rolling a 4 is 0.15.
The relative frequency of rolling a 5 is 0.15.
The relative frequency of rolling a 6 is about 0.13.
The relative frequencies of rolling 1, 2, 3, 4, 5, and 6 are quite similar. So, the relative frequency is a good predictor of the theoretical probability.
Step-by-step explanation:
this is exact answer from edmentum so change it up a bit
2. Select all expressions that can be subtracted from 9x to result in the expression
3x + 5.
A. -5 + 6x
B) 5 – 6x
С.) 6х +5
D. 6x - 5
E. -6x + 5.
Answers
Answer:
D. 6x-5
Step-by-step explanation:
I am not actually 100% but subtracting 6x from 9x will give you 3x and subtracting -5 will give you +5... SOOO. cross your fingers. lol
Solve for x....................................
Answers
Answer:
x = 4.5 is the answer to the question
PLEASE!!
What is the COMBINED surface area of the prisms shown below?
Answers
through: (5,-1) and (-3,-5)
Answers
Answer:
If you are trying to find slope the answer is 1/2
Step-by-step explanation:
I'm sorry if im wrong but thats if you're trying to find slope if you're not my bad.
(
5
,
−
1
)
(
5
,
-
1
)
with vertex
(
−
3
,
5
)
(
-
3
,
5
)
using the vertex form
y
=
a
(
x
−
h
)
2
+
k
y
=
a
(
x
-
h
)
2
+
k
.
Standard Form:
y
=
−
3
32
x
2
−
9
16
x
+
133
32
y
=
-
3
32
x
2
-
9
16
x
+
133
32
Vertex Form:
y
=
−
3
32
(
x
+
3
)
2
+
5
y
=
-
3
32
(
x
+
3
)
2
+
5
Helppppp pleaseeee xxxxx
Answers
Answer:
a. 28π m²
b. 44π m²
Step-by-step explanation:
a. Lateral surface of the cone = πrl
Where,
r = 4 m
l = 7 m
Lateral surface area = π*4*7 = 28π m²
b. Surface area of cone = πr(l + r)
r = 4 m
l = 7 m
Surface area = π*4(7 + 4)
= 4π(11)
= 44π m²
A hexagonal prism has a base with an area of 15 square inches and the volume is 105 cubic inches.
.
Complete the sentence about the height of the prism.
The height of the prism is _____ inches,square inches,cubic inches
Answers
Answer:
I believe the answer would be 1575 cubic inches. Sorry if i'm wrong!
Answer:
The answer is 7 square in
Step-by-step explanation:
Do this formula
V=Bh
105=15h
h=7 square in
The answer to this question
Answers
PLEASE ANSWER ASAP! 15 POINTS ! NO SCAM LINKS OR REPORTED :)
Answers
Answer: C
Step-by-step explanation: You have to plug in the values to see if it matches the values on the table of values
Which of the fractions is equivalent to 2/3
Answers
Answer:
4/6
6/9
12/18
8/12
5/10
Step-by-step explanation:,,
Answer:
The answers are 4/6 and 6/9.
Step-by-step explanation:
what is the answer. Evalute (2/3)2. Thank you
Answers
Answer:
4/3
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
[tex] { \frac{2}{3} }^{2} = \frac{4}{9} [/tex]
have a nice day
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
Answers
Answer:
864 inches cubed
Step-by-step explanation:
Since the volume is the 3 units multiplied together, 16 x 9 x 6 is 864.
Find the missing side of each triangle
I can’t remember the steps to doing this/the formula, an explanation would be great thanks!
Answers
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2
2^2+6^2=x^2
4+36=x^2
40=x^2
[tex]\sqrt{40}=x[/tex]
[tex]2\sqrt{10}[/tex][tex]=x\\[/tex]
Hope that helps :)
Answer:
sqrt(40) or approx. 6.324555
Step-by-step explanation:
a^2 + b^2 = c^2 (Pythagorean Theorem)
6 is a, 2 is b, and x is c, or the hypotenuse.
Plug in the values
6^2 + 2^2 = x^2
Simplify
36 + 4 = x^2
40 = x^2
Square root both sides
sqrt(40) = x
you guy have any song requests?
Answers
Answer:
Never want to give you up
Step-by-step explanation:
Brainliest? pls
Famous Dex - Pick It Up (Lyrics) feat. A$AP Rocky
My ordinary life
SoFaygo - Knock Knock
Streets
D !ck
Proving triangles similar
Answers
Answer: AA
Step-by-step explanation:
You can do vertical angles or alternate interior angles. Hope this helps :)
Find the common difference of the arithmetic sequence -7, -1, 5, ...
Answers
Answer:
d = -6
Step-by-step explanation:
common difference, d = -7-(-1) = -6
Rana sells 192 cakes in the ratio small: medium: large = 7 : 6 : 11.
The profit for one medium cake is twice the profit for one small cake.
The profit for one large cake is three times the profit for one small cake.
Her total profit is £532.48
Work out the profit for one small cake
Answers
Answer:
S = £1.28
Step-by-step explanation:
Let the small, medium and large cakes be S, M and L respectively.
Given the following data;
Total profits = £532.48
Total number of cake = 192 cakes
Ratio of S:M:L = 7:6:11
Sum of ratio = 7+6+11 = 24
To find number of each cakes, we would divide the total number of cakes by the sum of ratio;
Number of each cakes = 192/24
Number of each cakes = 8
Next, we determine the exact number of each type of cakes.
Small = 7*8 = 56 cakes.
Medium = 6*8 = 48 cakes.
Large = 11*8 = 88 cakes.
For the profits;
Translating the word problem into an algebraic expression, we have;
M = 2S
L = 3S
56S + 48*(2S) + 88*(3S) = £532.48
56S + 96S + 264S = 532.48
416S = 532.48
S = 532.48/416
S = £1.28
Therefore, the profit for one small cake is £1.28
The probability that Scott will win his next tennis match is 3/5
What is the probability that he will not win?
Answers
Answer:
the probability that he will not win is 2/5 cause it's just the chance that he doesn't win