Answers
The mapping diagram above does not represent a function since for each number in Set A (the input) where there are multiple mappings from Set B (the output).
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).
Based on the mapping diagram shown above, we can reasonably infer and logically deduce that the inputs (4, 3), (-2, 3), (8, 6), and (4, 7) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).
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Related Questions
graph the line that passes through the points (0,-8) and (5,-5) and determine the equation of the line
*I can graph it, I just need the equation*
Answers
The linear equation that passes through the points (0,-8) and (5,-5) is:
y = (3/5)*x - 8
How to find the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have the two points: (0,-8) and (5,-5)
Then the slope is:
a = (-5 + 8)/(5 - 0) = 3/5
And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:
y = (3/5)*x - 8
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skye is laying a brick barrier around a circular flower bed with a radius of 4 yards. Which of the following expression can be used to find the circumference around the flower bed in yards? Circle ALL that apply.
A 2xn B 4xn C 2x4xn D 8xn
Answers
The circumference around the flower bed in yards is D) 8×π.
What is the circumference of the circle?
The circumference of a circle is defined as the linear distance around it.
The formula for the circumference of a circle is [tex]2\pi r[/tex]. Where r is the radius of the circle.
It is given that the radius of the flower bed is 4 yards.
The flower bed is in the shape of a circle.
The circumference of the flower bed is 2×π×r.
Substitute the value of r in the equation.
Therefore the circumference around the flower bed is 8×π.
The correct option is D) 8×π.
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There are 17 houses on 1 block. How many houses are on 23 blocks?
Answers
By using multiplication, it can be calculated that
There are 391 houses in 23 blocks
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.
This is a word problem on multiplication
Number of houses in one block = 17
Assuming there are equal number of houses in each block,
Number of houses in 23 blocks = 23 [tex]\times[/tex] 17 = 391
There are 391 houses in 23 blocks
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A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 7700 kilograms have already been loaded into the container. Use the drop-down menu below to write an inequality representing cc, the total number of 40-kilogram crates that can be loaded into the shipping container.
Answers
An inequality representing c, the total number of 40-kilogram crates that can be loaded into the shipping container is; 7700 + (40c) ≤ 27500
The maximum number of 40 kg crate is 380.
How to solve Inequality Word Problems?We are given;
Weight of the crate = 40 kg
Greatest weight that the container can load = 27500 kg
Weight of the other shipments on the container = 7700 kg
The greatest number of 40 kg crates is represented by the letter "c".
Thus;
The weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container
Plugging in the relevant values gives;
7700 + (40c) ≤ 27500
7700 + 40c ≤ 23000
40c ≤ 27500 - 7700
40c ≤ 19800
c ≤ 19800/40
c ≤ 495
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What percent of 200 is 104?
Answers
Answer:
52%
Step-by-step explanation:
What percent of 200 is 104?
104/200 = 0.52
0.52 = 52%
How do you convert 2−2i to polar form?
Answers
2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]
To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:
Find the magnitude (or absolute value) of the complex number. This is the distance from the origin to the point representing the complex number in the complex plane. The magnitude of 2 - 2i is approximately 2.83.Find the argument of the complex number. This is the angle between the positive real axis and the line connecting the origin to the point representing the complex number in the complex plane. To find the argument, you can use the inverse tangent function (also known as arctangent or atan). The argument of 2 - 2i is approximately -135 degrees, or -2.356 radians.Combine the magnitude and argument to express the complex number in polar form. In polar form, a complex number is written as "magnitude (angle)", where the angle is expressed in either degrees or radians. So, the polar form of 2 - 2i is approximately 2.83 (-135 degrees) or 2.83 (-2.356 radians).To learn more about complex number, visit:
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what is the minimum sample size required to estimate a population mean with a confidence of 95%, if the margin of error is 2 units and a standard deviation of 10 units? show formula and your calculations. round to the next whole number.
Answers
The minimum sample size required to estimate a population mean with a confidence of 95%, a margin error of 2 units and a standard deviation of 10 units is 96.
A minimum sample size is the number of participants one needs to maintain their target confidence interval (margin of error) and confidence level while obtaining results that accurately represent the population they are studying.
The formula to calculate the minimum sample size for the population mean is [tex]\bold{n=\left(\frac{z\times \sigma}{E}\right)^2}[/tex]. Here, n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin error.
Given, the z-value for 95% confidence is 1.96, E is 2 and σ is 10.
Then, the minimum sample size is,
[tex]\begin{aligned}n&=\left(\frac{1.96\times10}{2}\right)^2\\&=(9.8)^2\\&=96.04\\&\approx96\end{aligned}[/tex]
The answer is 96.
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In AGHI, GI is extended through point I
to point J, m/IGH = (x+16)°,
m/HIJ = (4x – 12)°, and
m/GHI= (x +10)°. Findm/GHI.
Answers
Applying the exterior angles theorem, the measure of angle GHI is: 29°.
What is the Exterior Angle Theorem?The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.
Given the following:
m<IGH = (x+16)°,
m<HIJ = (4x – 12)°,
m<GHI= (x +10)°
Therefore:
m<HIJ = m<IGH + m<GHI
Substitute:
4x - 12 = x + 16 + x + 10
4x - 12 = 2x + 26
4x - 2x = 12 + 26
2x = 38
2x/2 = 38/2
x = 19
m<GHI= (x +10)° = 19 + 10 = 29°
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Which models represent 56 as a sum of fractions with a common denominator of 6?
Answers
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable
Step-by-step explanation:
j
In a circle, an angle measuring 8.7 radians intercepts an arc of length 3.9. Find the radius of the circle to the nearest 10th.
Answers
Answer:
r = .5 units
Step-by-step explanation:
8.7 R is an improper FRACTION of the 2 pi R of the entire circle ....set up a ratio:
8.7 / (2 pi) = 3.9 / x where x is the entire circumference measurement
x = 3.9 / (8.7 / (2 pi) ) = 2.82 units
To find the radius circumf = 2 pi r
2.82 = 2 pi r shows r = .5 units
how many ways can you distribute 6 faceless players over 4 servers (each of the servers are identical)?
Answers
Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.
1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.
2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.
3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.
4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.
There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.
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what is the slope-intercept form of the function described by this table? x 1 2 3 4 y 1 −2 −5 −8 enter your answer by filling in the boxes. y = x
Answers
The function depicted in the table has the following slope-intercept form:
y = -3x + 4
Explain the equation of straight line?The formula for a straight line is y=mx+c where c is the slope at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.For such equation of every straight line, the slope-intercept form is provided by:
y = mx +c
where:
The slope of the line is m.b is the line's y-intercept.Choose 2 points from the provided table, such as (2,-2) and (3,-5) and to use the evidence that the slope is, to determine the line's slope.
m = (y2 - y1)/(x2 - x1)
m = -5 + 2 / 3 - 2
m = -3
You can use the point (2,-2) or other point listed in the table along with this relation, to determine the y-intercept b.
b = y1 - mx1
b = (-2) -(-3 + 2)
b = 4
Consequently, is the function represented by the table's slope-intercept form: y -3x + 4.
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Alejandro, a pharmaceutical sales representative, sells statins for a drug maker. He earns a 12% commission of the total sales of the statins that he sells to hospitals. If he earned 60,000 in commissions, what was the total dollar value of the drugs that he sold?
Answers
Answer: x=500,000
Step-by-step explanation:
60,000=.12x
60,000/.12=x/.12
500,000=x
Sarah is trying to find the best deal for her phone service. She narrowed down the choices to the two companies in the table. Both companies charge per-minute rates, and there are no additional costs.
A 2-column table with 2 rows. Column 1 is labeled Company A with entries 18 dollars, 120 minutes. Column 2 is labeled Company B with entries 21 dollars, 150 minutes.
Sarah wants to know which company costs the least amount per minute.
Which quotients should Sarah find? Check all that apply.
StartFraction 120 Over 8 EndFraction
StartFraction 18 Over 120 EndFraction
StartFraction 150 Over 21 EndFraction
StartFraction 21 Over 150 EndFraction
Answers
For Sarah to know the company that costs the least amount per minute, the quotients she should find are:
B. 18/120D. 21/150.What is the quotient?The quotient is the result of a division operation.
A division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
A division operation has four parts:
The dividend (the number or value being divided or numerator).The divisor (the number or value dividing or denominator).The equal symbol (showing that the solution is equal to the mathematical expressions).The quotient (the result of the division operation).Company A Company B
Total charge $18 $21
Total minutes 120 150
Per-minute rate $0.15 ($18/120) $0.14 ($21/150)
Thus, the quotients Sarah should find are Options B and D.
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find the relative maxima and relative minima, if any, of the function. (if an answer does not exist, enter dne.) g(x)
Answers
The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.
Given:
Function g(x) = x^3 - 48x + 4
Take the derivative and set it equal to zero
3x^2 - 48 = 0
x^2 = 48/3 = 16
x = sqr16 = ±4
At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124
Point (4,-124) is a local or relative minimum
At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122
The point (-4, 22) is a local or relative maximum
Refer to this complete question:
Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?
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How do you write 0.09 as a fraction?
Answers
Answer:
9/100
Step-by-step explanation:
numerator = whole number
denominator = 100
9/100
$89.75 scooter ; 7.25% tax
Answers
Answer: $96.25
Step-by-step explanation:
Take 89.75 divided by 100% = 0.8975
Then times 7.25% = $6.5
Total is 89.75 + 6.5 = $96.25
franz and his friends are using the spinners below to play a game. if one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
Answers
The possible outcomes for one turn is a table with 4 columns and 3 rows. First Spinner is the label for the columns, and Second Spinner is the label for the rows. Entries 2 A, 2 B, and 2 C are in Column 1. 4A, 4B, and 4C are the entries in Column 2. 6A, 6B, and 6C are entries in column 3. 8A, 8B, and 8C are the entries in column 4. a 2-row, 4-column table.
How many possible outcomes are there in the spinner?The spinner is divided into a total of 8 pieces. Consequently, there are 8 total outcomes. We express our likelihood as a fraction out of 8No. There are seven components overall and one white piece. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. So, it has an 18 percent chance of happening. Every rotation is distinct. The sum of the results from each event will give you the total number of outcomes for two or more events. The reason why this entails multiplication to find a product is why it is known as the "product rule for counting." Every time, one fourth of the time, the spinner will land on a different color.To the complete question is
franz and his friends are using the spinners below to play a game. if one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
1. A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B. Column 2 has entries 4 A, 4 B. Column 3 has entries 6 A, 6 B. Column 4 has entries 8 A, 8 B.
2. A 4-column table with 3 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B, 2 C. Column 2 has entries 4 A, 4 B, 4 C. Column 3 has entries 6 A, 6 B, 6 C. Column 4 has entries 8 A, 8 B, 8 C. A 4-column table with 2 rows.
3.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2, A. Column 2 has entries 4, B. Column 3 has entries 6, C. Column 4 has entries 8, D. A 4-column table with 3 rows.
4.The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 A, 2 A. Column 2 has entries 4 B, 4 B, 4 B. Column 3 has entries 6 C, 6 C, 6 C. Column 4 has entries 8 A, 8 B, 8 C.
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T=4m^2 - 11 Work out the value of T when m = -3
Answers
Answer: T=25
Step-by-step explanation:
T=4m^2 -11
We know that m= -3
-3^2 = 9
So the equation is T=4 (9) -11
T = 36 -11
T= 25
how to solve - |x + 5| < -17
Answers
Answer:
x∈(−∞,−22)∪(12,+∞)
Step-by-step explanation:
Evaluate
−∣x+5∣<−17
Calculate
∣x+5∣>17
Separate the inequality into 2 possible cases
x+5>17x+5<−17
Solve the inequality for x
x>12x+5<−17
Solve the inequality for x
x>12x<−22
Solution
x∈(−∞,−22)∪(12,+∞)
Which of the following is NOT a criterion for similarity?
A. AA postulate
B. SAS postulate
C. SSS postulate
D. RHS postulate
Answers
Answer:
Answer Option A: AA Postulate
All other options prove two triangles are similar; however, the RHS Postulate proves two right-angle triangles to be congruent, not similar.
i'll mark brainliest!!!!!!
Answers
The solution is Option D.
The equation of line that passes through the point P ( 4 , -3 ) and the point Q ( 0 , -2 ) is y = ( -1/4 )x - 2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first point be P = P ( 4 , -3 )
Let the second point be Q = Q ( 0 , -2 )
Now , the slope of the line passing through the points is calculated from the formula slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -2 - ( -3 ) ) / ( 0 - 4 )
Slope m = ( -2 + 3 ) / -4
Slope m = -1/4
Now , the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -3 ) = ( -1/4 ) ( x - 4 )
On simplifying the equation , we get
y + 3 = ( -1/4 )x + 1
Subtracting 3 on both sides of the equation , we get
y = ( -1/4 )x - 2
Therefore , the value of A is y = ( -1/4 )x - 2
Hence , the equation of line is y = ( -1/4 )x - 2
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[tex]6x^{2} = 6[/tex]
Answers
[tex]6x^2=6[/tex]
Divide both sides by 6:
[tex]\dfrac{6x^2}{6} =\dfrac{6}{6}[/tex]
[tex]x^2=1[/tex]
Take square root:
[tex]x=\pm\sqrt{1}[/tex]
[tex]\fbox{x = 1 or x = -1}[/tex]
A rectangle has sides of (4x + 13) and (5x – 2). What is the area of the rectangle?
Answers
Answer:
Below
Step-by-step explanation:
The area is just the two side lengths multiplied together
area = (4x+13)(5x-2) = 20x^2 +57x -26 units^2
Mrs. Wu's car is completely out of gas. Gas costs $3.56 per gallon, and the car's gas tank can hold 12.5 gallons. How much money will Mrs. Wu spend to fill the gas tank?
Answers
Answer:It will cost Mrs. Wu $44.5 to fill the gas tank.
Step-by-step explanation: 3.56x12.5= 44.5
How do you solve 14p−8=22+20p ?
Answers
The value of p is -5
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
[tex]14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5[/tex]
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which of the following represents the average rate of change to the function g(x) = 3/2x + 1 over the interval -2 < x < 8
Answers
The average rate of change to the function is (d) 3/2
How to determine the average rate of change to the function?From the question, we have the following parameters that can be used in our computation:
g(x) = 3/2x + 1
Also, we have the interval to be
-2 < x < 8
This interval can be expressed as
a = -2 and b = 8
So, we start by calculating g(-2) and g(8)
Substitute the known values in the above equation, so, we have the following representation
g(-2) = 3/2 * (-2) + 1
g(-2) = -2
Also, we have
g(8) = 3/2 * (8) + 1
g(8) = 13
The average rate of change to the function is then calculated as
Rate = [g(8) - g(-2)]/[8 + 2]
So, we have
Rate = (13 + 2)/(8 + 2)
Evaluate
Rate = 3/2
Hence, the average rate is 3/2
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erin wants to find the circumference of a circle with radius 7cm . which of following can she use to find the circumference of the circle ?
A. 2x 7 x π
B 2 x 14 x π
C 7/2 x π
D 14 xπ
E. 49 x π
Answers
To find the circumference of a circle with a radius of 7 cm, Erin should use 2×7×π. This is because the circumference of a circle is calculated by the formula 2×π×r.
What is the circumference of a circle?The circumference is the measure of the perimeter of a circle. Since we know that from every point on the circle to its center has an equal length and is said to be its radius, the perimeter of the circle we can write as
Circumference = 2 × π × r units.
Here r is the radius of the circle.
Calculation:It is given that Erin wants to find the circumference of a circle with a radius of 7 cm.
So, first, she has to know the formula for finding the circumference.
Here the radius is given as 7 cm i.e., r = 7 cm
Then, the circumference of the given circle is
= 2 × π × r
On substituting the radius value into the above formula, we get
Circumference = 2 × π × 7 cm
⇒ 14π cm
So, she needs to use option A. 2 × 7 × π for finding the required circumference. This is the first step for finding the circumference of a circle.
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(c) Compute and interpret the mean of the random variable x The mean is activities (Type an integer or a decimal Do not round.) Which of the following interpretations of the mean is correct? O A. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable O B. The observed value of an experiment wil be equal to the mean of the random variable in most experiments O C. As the number of experiments increases, the mean of the observations will approach the mean of the random variable OD. The observed value of an experiment will be less than the mean of the random variable in most experiments (d) Compute the standard deviation of the random variable x The standard deviation is activities (Round to one decimal place as needed )
Answers
The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.
Mean of random Variable x :
The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.
Standard Deviation of Random Variable:
A measure of the variance of a random variable distribution that determines how for a value is from its expected value.
The standard deviation of a random variable X is often written as σ or σₓ.
For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.
In symbols σ = √ (x - μ)² P(X =x)
The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]
The square of the standard deviation equals the variance Var(X) = σ².
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[r] bastien, inc. has been manufacturing small automobiles that have averaged 45 miles per gallon of gasoline in highway driving. the company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 45 miles per gallon in highway driving. an independent testing service road-tested 52 of the automobiles. the sample showed an average of 46.1 miles per gallon. the sample standard deviation is 5.3 miles per gallon. conduct an appropriate hypothesis test. find the t-statistic and the appropriate conclusion at the 0.01 level of significance.
Answers
According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)
where,
[tex]X_{avg}[/tex] = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
[tex]X_{avg}[/tex] = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
H0 = p<= 45 : miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
HA : p > 45 : miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
T = (X - p)/(SD/√n)
where,
X = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
X = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
T = 46.1-45/(5.2/√52)
T = 1.1/0.735
T = 0.634
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
To learn more about hypothesis test visit brainly.com/question/17347077
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