The probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days is 0.0075
The situation you are describing follows a binomial distribution with parameters n = 15 and p = 0.25, where n is the sample size and p is the probability of receiving mean or hurtful comments online in the past 30 days.
We want to find the probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days. This can be expressed as
P(X > 7) = 1 - P(X ≤ 7)
where X is the number of undergraduates in the sample who say that they have received hurtful comments online in the past 30 days.
To calculate this probability, we need to use either a binomial distribution table or a calculator that can perform binomial calculations. Using a binomial distribution table, we can find that
P(X ≤ 7) = 0.9925
Therefore,
P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.9925 = 0.0075
Learn more about probability here
brainly.com/question/29350029
#SPJ4
The given question is incomplete, the complete question is:
A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. The rate at your university matches this 25%. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days?
if the given triangles are similar find the missing length
The length of PQ in triangle PQR is 110.
What are similar triangles ?
Similar triangles are two triangles that have the same shape but may differ in size. In other words, their corresponding angles are equal, and their corresponding sides are in proportion. This means that if you were to resize one triangle by a constant factor, the resulting triangle would still be similar to the original triangle.
For example, if you take a triangle and multiply all its side lengths by a factor of 2, you will end up with a triangle that is twice as large but still similar to the original triangle.
According to the question:
Since the triangles XYZ and PQR are similar, their corresponding sides are in proportion. That is:
XY/PQ = XZ/PR = YZ/QR
We can use this property to find the length of the missing side QP.
First, let's find the ratio of corresponding sides:
XY/PQ = XZ/PR
48/PQ = 55/110
Simplifying this equation, we get:
PQ = 48*110/55 = 96
So, PQ is 96.
Alternatively, we could use the other pair of corresponding sides:
XZ/PR = YZ/QR
55/110 = 73/146
Simplifying this equation, we get:
QP = 55*146/73 = 110
So, QP is also 110.
To know more about similar triangles visit:
https://brainly.com/question/29249755
#SPJ1
Which angle is an alternate exterior angle to ∠8? ∠3 ∠4 ∠5 ∠6
There is no alternate exterior angle corresponding to ∠8. ∠3 ∠4 ∠5 ∠6 are not an alternate exterior angle to ∠8
We know that alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal,
here, we have,
We have been given a geometrical figure as shown in the image.
Now we know that a pair of alternate exterior angles exist for a pair of parallel lines.
Hence, there is no alternate exterior angle corresponding to ∠8.
Therefore, there is no alternate exterior angle corresponding to ∠8.
To learn more about angles, click here:
brainly.com/question/28451077
#SPJ4
The following chips are placed in a bucket: 4 red, 1 yellow, 5 blue, and 5 green. One chip is randomly selected from the bucket.
What is the probability that the chip is blue?
Answer:Red
Step-by-step explanation:
Answer:
Step-by-step explanation:
5 blue out of 15 chips
a quality control inspector has drawn a sample of 16 light bulbs from a recent production lot. suppose 20% of the bulbs in the lot are defective. what is the probability that between 6 and 9 (both inclusive) bulbs from the sample are defective? round your answer to four decimal places.
The probability that between 6 and 9 (both inclusive) bulbs from the sample are defective is 0.5362
This is a binomial distribution problem, where the probability of success (defective bulb) is 0.2 and the probability of failure (non-defective bulb) is 0.8. We need to find the probability that between 6 and 9 (both inclusive) bulbs out of 16 bulbs in the sample are defective.
We can use the binomial probability formula to solve this problem
P(6 ≤ X ≤ 9) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
where X is the number of defective bulbs in the sample.
P(X = k) = (n choose k) × p^k × (1-p)^(n-k)
where n is the sample size, k is the number of defective bulbs, p is the probability of a defective bulb, and (n choose k) is the binomial coefficient.
Using this formula, we can calculate the probability for each value of X and sum them up to get the probability for the range 6 to 9.
P(X = 6) = (16 choose 6) × 0.2^6 × 0.8^10 = 0.0881
P(X = 7) = (16 choose 7) × 0.2^7 × 0.8^9 = 0.1409
P(X = 8) = (16 choose 8) × 0.2^8 × 0.8^8 = 0.1606
P(X = 9) = (16 choose 9) × 0.2^9 × 0.8^7 = 0.1462
Therefore, the probability that between 6 and 9 (both inclusive) bulbs from the sample are defective is
P(6 ≤ X ≤ 9) = 0.0881 + 0.1409 + 0.1606 + 0.1462 = 0.5362
Learn more about probability here
brainly.com/question/29350029
#SPJ4
B(-1;7) , C(x;-1) and D(1;8) : B,C and D are collinear
The coordinates of point C are (17, -1).
how to find slope of line when two points are given ?let say a line have two points A (x1,y1) and B(x2,y2)
slope of line AB = (y2 - y1) / (x2 - x1)
Now given that points B, C, and D are collinear, then they lie on the same straight line. This means that the slope of the line passing through any two of the points will be the same as the slope of the line passing through the other two points. We can use this fact to find the value of x.
The slope which is between points B and C is:
slope of line BC = (y2 - y1) / (x2 - x1) = (-1 - 7) / (x - (-1)) = -8 / (x + 1)
The slope which is between points C and D is:
slope of line CD = (y2 - y1) / (x2 - x1) = (8 - (-1)) / (1 - x) = (9) / (1 - x)
Since B, C, and D are collinear, slope of BC = slope of CD. Therefore:
-8/(x+1) = 9/(1-x)
by solving the x, we get:
-8(1 - x) = 9(x + 1)
-8+8x=9x + 9
x = 17
So, the coordinates of point C are (17, -1).
To know more about coordinates visit:
brainly.com/question/27749090
#SPJ9
20 Points:
How many ways are there to form a 5 person committee from 2 freshmen, 3 sophomores, 2 juniors, and 2 seniors if there cannot be the same number of juniors and seniors? Note that people are distinct.
=================================================
Explanation:
2 freshmen + 3 sophomores + 2 juniors + 2 seniors = 9 students total.
Let's consider the cases where we have the same number of juniors and seniors. We'll then take the complement of this to get the final answer.
Case A will look at having 1 of each junior and senior.Case B will look at having 2 each of juniors and seniors.-----------
Case A: There is 1 junior and 1 senior
There are 2 ways to pick a junior and 2 ways to pick a senior. That's 2*2 = 4 ways so far.
Then we have 9-4 = 5 students left to pick from (i.e. 2 freshmen+3 sophomores = 5 students left) and we have 5-2 = 3 seats to fill. Order doesn't matter on the committee since each person has equal rank.
We use the nCr combination formula.
n = 5 students
r = 3 seats to fill
n C r = (n!)/(r!(n-r)!)
5 C 3 = (5!)/(3!*(5-3)!)
5 C 3 = (5!)/(3!*2!)
5 C 3 = (5*4*3!)/(3!*2!)
5 C 3 = (5*4)/(2!)
5 C 3 = (5*4)/(2*1)
5 C 3 = (20)/(2)
5 C 3 = 10
There are 10 ways to fill the remaining 3 seats when we pick from the freshmen and sophomores only.
To recap everything so far:
4 ways to pick the 1 junior and 1 senior10 ways to pick the 3 other students (freshmen + sophomores)Therefore, we have 4*10 = 40 different combinations possible for case A. We'll refer to this value later.
-----------
Case B: We pick 2 juniors and 2 seniors
Since there 2 juniors to pick from, and 2 junior seats to fill, there's only 1 way to do this. Likewise, there's only 1 way to pick the 2 seniors to fill the 2 seats.
In total so far there is 1*1 = 1 way to pick the 2 juniors and 2 seniors in any order you like.
Then we have 9-4 = 5 students left that are freshmen or sophomores. This is the number of choices we have for the final 5th seat.
We have 1*5 = 5 ways to have case B happen.
----------
Summary so far:
40 ways to do case A5 ways to do case B40+5 = 45 ways to do either case.There are 45 ways to have the same number of juniors as seniors (either 1 of each or 2 of each).
Now we must calculate the number of total combinations possible on this committee. We'll turn to the nCr formula again.
n = 9 students
r = 5 seats
n C r = (n!)/(r!(n-r)!)
9 C 5 = (9!)/(5!*(9-5)!)
9 C 5 = (9!)/(5!*4!)
9 C 5 = (9*8*7*6*5!)/(5!*4!)
9 C 5 = (9*8*7*6)/(4!)
9 C 5 = (9*8*7*6)/(4*3*2*1)
9 C 5 = (3024)/(24)
9 C 5 = 126
There are 126 different five-person committees possible.
Of those 126 committees, 45 of them consist of cases where we have the same number of juniors and seniors.
That must mean there are 126-45 = 81 combinations where we do not have the same number of juniors and seniors. This is where the concept of "complement" comes in.
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000. Which statements regarding function S are true? Select TWO that apply. Responses A. S(10)=S(5) means that there were the same number of students in 2010 as in 2005. B. S(3)= 2,015 means that there were 3 students in the year 2015. C. S(15) − S(10) = −40 means that there were 40 less students in 2010 than there were in 2015. D. S(5)= 2,024 means that there were 2,024 students in the year 2005. E. S(0) = 2,000 means that there were no students in the year 2000.
Answer:
The correct responses are:
A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.
E) S(0) = 2,000 means that there were no students in the year 2000.
B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.
Which value of x makes the expression 3√53x
equivalent to 21√53?
The value of x that makes the expression 3√(53x) equivalent to 21√53 is 49.
What does expression mean?In mathematics, an expression is a combination of numbers, variables, and operations, typically written using mathematical symbols and/or mathematical notation. An expression can be a single number, variable, or combination of the two, or it can be a more complex combination of numbers, variables, and operators such as addition, subtraction, multiplication, division, exponentiation, or root extraction. Expressions can be used to represent a wide variety of mathematical concepts and relationships, such as equations, inequalities, functions, and geometric figures. They are an important part of mathematical language and are used to communicate mathematical ideas and concepts.
What does equation mean?In mathematics, an equation is a statement that shows the equality of two expressions. It typically involves one or more variables and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or root extraction. The expressions on both sides of the equation are separated by an equal sign (=), indicating that they have the same value. The purpose of an equation is to find the value of the variable(s) that makes the equation true. Solving an equation involves manipulating the expressions on both sides of the equation to isolate the variable and determine its value. Equations are used in a wide variety of mathematical applications, such as solving problems in algebra, geometry, calculus, and physics.
According to the given informationWe can start by equating the expression 3√(53x) to 21√53 and then solving for x.
3√(53x) = 21√53
Dividing both sides by 3√53, we get:
√x = 7
Squaring both sides of the equation, we get:
x = 49
To know more about the equation visit:
brainly.com/question/10049598
#SPJ9
I need helppppppppp please help me
Answer:
12.9cm
Step-by-step explanation:
Trapeziums QRVW and QRSP are similar because they share the same side 5.5 cm and their angles are corresponding to each other.
We can express the ratios of sides in both trapeziums to find WV.
Since side 5.5 is the same in each trapezium,
[tex]\frac{5.5}{WV}=\frac{5.5}{12.9}[/tex]
Thus, WV = 12.9cm
Hope this helps:)
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To model the given data points, we can use a linear function of the form y = mx + b.
First, we need to find the slope (m) of the line:
m = (y2 - y1) / (x2 - x1)
m = (-6 - (-2)) / (1 - 0)
m = -4/1
m = -4
Now, we can use the slope and one of the points to find the y-intercept (b):
y = mx + b
-2 = (-4)(0) + b
b = -2
Therefore, the linear function that models the given data is:
y = -4x - 2
Please show workkk!!!
Answer:
$104.11
Step-by-step explanation:
To calculate the monthly payment for a loan, we can use the following formula:
Monthly payment = (Pr(1+r)^n) / ((1+r)^n-1)
where:
P = the principal amount (the amount borrowed)
r = the monthly interest rate (annual interest rate divided by 12)
n = the number of payments (total number of years multiplied by 12)
In this case, the principal amount is $3825, the annual interest rate is 15%, and the loan term is 4 years. So we have:
P = $3825
r = 0.15/12 = 0.0125
n = 4*12 = 48
Substituting these values into the formula, we get:
Monthly payment = (38250.0125(1+0.0125)^48) / ((1+0.0125)^48-1)
Monthly payment ≈ $104.11
Therefore, the monthly payment for a $3825 loan at 15% annual interest for 4 years is approximately $104.11.
5 Divided 1/4 As a Area Model
(A area model please)
Answer: You can comment if this is wrong but I don't know what an area model is entirely I might just I don't remember
|\ |\
| \ | \
| \| \
|___\|___\
1/4 1/5
Step-by-step explanation:
1. Draw a rectangular area model with two sections.
2. Label the left section with 1/4 and the right section with 1/5.
3. Divide the left section into 4 equal parts by drawing lines horizontally and vertically
4. Divide the right section into 5 equal parts by drawing lines horizontally and vertically.
5. Count the number of parts in the left section (4 parts) and the number of parts in the right section (5 parts).
6. Multiply the parts in the left section by the parts in the right section, which gives 4 x 5 =20.
7. The answer is 20/4 = 5.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y=16x^2+173x+140
An equation is formed of two equal expressions. The maximum height reached by a rocket, to the nearest tenth of a foot is 1542.82 feet.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
To find the maximum height through which the rocket will reach, we need to differentiate the given function, therefore, we can write,
y=-16x²+173x+140
dy/dx = -16(2x)+173
Substitute the value of dy/dx as 0, to get the value of x,
0 = -32x + 173
173 = 32x
x =5.406
Substitute the value of x in the equation to get the maximum height,
y=-16x²+173x+140
y=-16(5.406²) +173(5.406) +140
y= 467.59 + 935.23 + 140
= 1542.82 feet.
Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 1542.82 feet.
To know more about equations, visit:
brainly.com/question/2263981
#SPJ9
what pattern of growth are we currently exhibiting? exponential growth intrinsic growth logistic growth none of the other answer options is correct. geometric growth
Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time.
Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time. This means that the growth rate is proportional to the current size or value of the quantity, resulting in a continuously increasing growth rate.
Geometric growth is commonly observed in natural and social systems, such as population growth, compound interest, and the spread of infectious diseases. It is represented mathematically by an exponential function, where the base of the exponent is greater than one, indicating an increasing rate of growth over time.
Learn more about Geometric growth here
brainly.com/question/13156498
#SPJ4
I have solved the question in general, as the given question is incomplete.
The complete question is:
What is geometric growth ?
Find the length of the hypotenuse of a 45°-45°-90° triangle with a leg
length of 8√8 centimeters
Answer:
Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.
Step-by-step explanation:
In a 45°-45°-90° triangle, the two legs are congruent, which means that each leg is equal to the length of the hypotenuse divided by √2.
Let h be the length of the hypotenuse. Then we have:
leg = h/√2
Given that one of the legs is 8√8 centimeters, we can substitute this value into the equation above to solve for h:
8√8 = h/√2
Multiplying both sides by √2, we get:
8√8 x √2 = h
Simplifying, we get:
h = 8√16
h = 8 x 4
h = 32
Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.
PLEASE HELPPPP GIVING BRAINLIEST IF CORRECT
Answer: B
Step-by-step explanation:
B. Find one possible point in the part of
the coordinate plane shown that could
be the fourth Vertex D of the
parallelogram. Give its coordinates.
Answer:(0,-1).
Step-by-step explanation:
As the diagonals of a parallelogram bisect each other, the midpoint of AC is the same as the midpoint of BD. Therefore, the fourth vertex D is (0,-1).
y = –5x + 10
y = –3x + 2
Answer:
Step-by-step explanation:
y = –5x + 10
y = –3x + 2
–5x + 10= –3x + 2
2x= 8
x=4
y= -5(4)+10
y= -20+10
y=(-10)
Answer:
Step-by-step explanation:
[tex]-5x + 10= -3x + 2[/tex] (since both equal y)
[tex]10=2x+2[/tex] ([tex]+5x[/tex] both sides)
[tex]8=2x[/tex] (-2 both sides)
[tex]x=4[/tex] (÷2 both sides)
Sub [tex]x=4[/tex] to find y:
[tex]y=-5(4)+10=-10[/tex]
Solution: x=4, y= -10
How do you find orthogonal projection on a line?
the orthogonal projection of a point P onto a line L can be expressed as: projection L(P) = ((P . u) ×u)·
Define orthogonal projectionOrthogonal projection is a mathematical operation that involves projecting a vector or point onto another vector or line in a way that the projection is perpendicular (or orthogonal) to the vector or line.
To find the orthogonal projection of a point on a line, you can follow these steps:Identify the point and the line: Let the point be P and the line be L.Find a vector that is parallel to the line: Let the vector be v.Find the unit vector that is parallel to the line: Normalize the vector v by dividing it by its magnitude to obtain the unit vector u.Find the vector from the origin to the point P: Let the vector be w.Calculate the dot product of w and u: This gives the magnitude of the projection of w onto u.Multiply u by the dot product obtained in step 5: This gives the projection vector.Add the projection vector to the origin: This gives the orthogonal projection of the point P onto the line L.In mathematical notation, the orthogonal projection of a point P onto a line L can be expressed as:
projection L(P) = ((P . u) × u)
To know more about parallel, visit
https://brainly.com/question/16701300
#SPJ1
what is the probability of selecting a striped marble, not replacing it, then selectinga balck marble?
The probability of selecting a striped marble, not replacing it, then selecting a black marble is 4/15.
The probability of selecting a striped marble on the first draw is 6/10, since there are 6 striped marbles out of a total of 10 marbles in the bag.
After the first marble is drawn, it is not replaced, so there are now 9 marbles left in the bag. Out of these, there are 4 solid marbles and 5 striped marbles. Therefore, the probability of selecting a black marble on the second draw is 4/9.
To find the probability of both of these events occurring together, we multiply the probabilities
P(striped, then black) = P(striped) × P(black | striped not replaced)
P(striped, then black) = (6/10) × (4/9)
P(striped, then black) = 24/90
P(striped, then black) = 4/15
Learn more about probability here
brainly.com/question/11234923
#SPJ4
The given question is incomplete, the complete question is:
There are 10 marbles in a bag (4 solid, 6 striped) .what is the probability of selecting a striped marble, not replacing it, then selecting a black marble?
3. Which translation moves point X so that
its image is on the y-axis?
A (x,y) → (x + 4, y + 8)
B (x,y) → (x-4, y + 8)
C (x, y) → (x+8, y + 4)
D(x, y) → (x+8, y - 4)
In addition, the image's y-coordinate would be , this indicates that we must raise the point by to align it with the y-axis. Hence, D is the right response.
What kind of coordinate is that?Option A moves the point 4 units horizontally and 8 units vertically, but does not move it onto the y-axis.
Option B moves the point -4 units horizontally and 8 units vertically, but does not move it onto the y-axis.
Option C moves the point horizontally by 8 units and vertically by 4 units, but it does not move it to the y-axis.
Option D moves the point 8 units horizontally and -4 units vertically. When we apply this transformation to an x-axis point, its y-coordinate remains unchanged, so the point's image is on the y-axis. As a result, option D is the correct translation:
(x, y) → (x+8, y-4)
To know more about coordinate visit:
brainly.com/question/27571390
#SPJ1
What is the rate of change of Y with respect to X for this function?
Answer:
-7/9
Step-by-step explanation:
its not a complete change to 1 but it is very close to being a 1
If a bag of 7 oranges weighs 35 ounces. How much does 1 orange weigh?
Answer:
1 orange weighs 5 ounces.
Divide
35÷7 = 5
so, one orange weighs 5 ounces.
pls anwser need helpppp
Question 5(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric
The answer of the given question based on the histogram is option (a) IQR, because Sunny Town is symmetric and option (b) IQR, because Beach Town is skewed.
What is Frequency?Frequency refers to the number of times a particular event or value occurs within a given dataset or sample. In statistics, frequency is often used to describe the distribution of a variable, where a frequency distribution shows the number of observations that fall into each category or interval.
The IQR (interquartile range) should be used for both sets of data to determine the location with the most consistent temperature. The IQR is a measure of spread that is not influenced by extreme values or outliers, which is helpful in comparing the consistency of temperatures in different locations. It is appropriate to use the IQR for Sunny Town because the data is roughly symmetric, and for Beach Town because although it is skewed, the IQR is more robust than the range and is not influenced by outliers.
To know more IQR (interquartile range) visit:
https://brainly.com/question/29077638
#SPJ1
A recent study1 examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with n=25 in each group: healthy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The data are in FootballBrain where the variable Hipp measures brain size as the volume of the hippocampus (in ml) for each subject.
Let group 1 be the football players with no concussion and group 2 be the football players with a history of concussions.
(a) State the null and alternative hypotheses.
(b) Use StatKey or other technology to find the value of the relevant sample statistic. Round your answer to one decimal place.
(c) Use StatKey or other technology to find the p-value. Round your answer to three decimal places.
(d) Does it appear that this difference in brain size is just due to random chance?
(b) The difference in sample mean is 0.544 ml. (c) Using StatKey, we find the p-value to be 0.046. (d) It is unlikely that this difference is due to random chance alone.
(a) The null hypothesis is that there is no difference in average brain size between football players with no history of concussions (FBNoConcuss) and football players with a history of concussions (FBConcuss). The alternative hypothesis is that the average brain size is larger in FBNoConcuss than in FBConcuss.
H0: μFBNoConcuss = μFBConcuss
HA: μFBNoConcuss > μFBConcuss
(b) The relevant sample statistic is the difference in sample mean between the two groups.
Therefore, the difference in sample mean is 0.544 ml.
(c) Using StatKey, we find the p-value to be 0.046.
(d) With a p-value of 0.046, which is less than the commonly used significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the average brain size is larger in FBNoConcuss than in FBConcuss. It is unlikely that this difference is due to random chance alone.
Learn more about null hypothesis :
https://brainly.com/question/28920252
#SPJ4
a political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. if the candidate wants a 1% margin of error at a 95% confidence level, what size of sample is needed? be sure to round accordingly. the candidate would need to survey people in the community in order to be within a 1% margin of error at a 95% confidence level.
In order to be within a 1% margin of error at a 95% confidence level, the candidate would need to survey 9604 people in the community. The size of the sample is 9604.
We have a political candidate who wants a 1% margin of error at a 95% confidence level. To find the size of the sample, we use the formula given below;
n = [ Z (α/2) / E ]²
Where,
n = the sample size required
Z (α/2) = the value obtained from the standard normal distribution for the given level of confidence
E = the margin of error
Here, α = 1 - 0.95 = 0.05
Z (α/2) = Z (0.025), is the z-value corresponding to 0.025 in the normal distribution table. It is found to be 1.96.
Now, substituting the given values in the formula,
n = (1.96² * 0.5 * 0.5) / 0.01² ⇒ 9604
Hence, the sample size required for the poll is 9604.
However, this is not feasible, as it would be very expensive and time-consuming. Therefore, we will round the answer to the nearest whole number as we are looking for a practical solution. Thus, the candidate would need to survey 9604 people in the community (rounded to the nearest whole number).
To know more about the "confidence level": https://brainly.com/question/15712887
#SPJ11
you decide to go to a rent-to-own company and purchase a laptop. the cost is $20.95 per month for 5 years. how much did you pay total at the end of the 5 years for the laptop?
You paid the total amount of $1257 at the end of 5 years.
Let us assume that c represents the cost per month.
So, c = $20.95
and let t represents the total number of months.
We know that there are 12 months in a year.
so, the number of months in 5 years would be:
12 × 5 = 60
So, t = 60 months
Using unitary method the total amount paid at the end of five years :
s = c × t
s = 20.95 × 60
s = $1257
Therefore, the total amount is $1257
Learn more about the unitary method here:
https://brainly.com/question/28276953
#SPJ4
M∠V=(2x+2) ∘ , and m ∠ W = ( 3 x + 4 ) ∘ m∠W=(3x+4) ∘. Find m ∠ V. M∠V
the measure of angle V is approximately 21.87 degrees. To find the measure of angle V, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:
m∠V + m∠W + m∠X = 180
where angle X is the third angle in the triangle formed by V, W, and X. We know that m∠W is (3x+4) degrees, and we can see that angle X is adjacent to angle V, so we can use the fact that the sum of adjacent angles is equal to the total angle to write:
m∠V + m∠X = (2x+2) degrees
Now we can substitute this expression for m∠X into the first equation to eliminate m∠X:
m∠V + (2x+2 - m∠V) + (3x+4) = 180
Simplifying and solving for x, we get:
5x + 6 = 180
5x = 174
x = 34.8
Now we can substitute this value of x back into our expression for m∠V + m∠X to find m∠V:
m∠V + (2(34.8)+2 - m∠V) = 71.6
Simplifying and solving for m∠V, we get:
3m∠V = 65.6
m∠V = 21.87 (rounded to two decimal places)
Therefore, the measure of angle V is approximately 21.87 degrees.
To know more about measure of angle click here:
brainly.com/question/16352647
#SPJ4