MCN= ACN-ACN-1 is the basis of diminishing marginal utility.
What is marginal utility?
The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.
When positive marginal utility occurs?When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.
According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."
So
MCN= ACN-ACN-1
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a survey was taken of a random sampling of residents of new york city and los angeles to compare how many of them own a car. a 4-column table with 3 rows. the first column has no label with entries l a residents, n y c residents, total. the second column is labeled own a car with entries 3,251; 1,478, 4,729. the third column is labeled do not own a car with entries 869; 6,182; 7,051. the fourth column is labeled total with entries 4,120; 7,660; 11,780. which statement about the two-way frequency table is true?
The true statement is;
There is a greater percentage of Los Angeles residents who own a car than New York City residents who do
Given,
Following is the presentation of the values:
The number of residents in Los Angeles own a car = 3251
The number of residents in New York City own a car = 1478
Total residents who own a car = 4729
Los Angeles residents who do not own a car = 869
New York City residents who do not own a car = 6182
Total residents who do not own a car = 7051
Total Los Angeles residents sampled = 4120
Total New York City residents sampled = 7660
Total residents of both cities sampled = 11780
Here,
Percentage of Los Angeles residents who own a car = (3251/4120)×100 = 78.9%
Percentage of New York City residents who own a car = (1478/7660)×100 = 19.3%
Then,
The total number of people in the poll who own a car = 4729
Therefore,
The correct option is that there is a greater percentage of Los Angeles residents who own a car than New York City residents who do.
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Answer: B
Step-by-step explanation:
solving systems by substation
x-4y=15
3x-12y=12
Answer:
There is no solution
Step-by-step explanation:
x - 4y = 15
3x -12y = 12
Times the first equation by -3
-3x +12y = -45
3x - 12y = 12
0 = -33
This is untrue; 0 is not equal to -33
So, there is no solution for this system.
If you can please give me a Brainliest, thank you, and have a good day!
HELP ME I WILL GIVE 20 POINTS PLS
the given proportional relationship y=0.5x with proportional constant is 1/2.
what is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.
So the equation will be y = kx
or y = 0.5(x)
Here proportional constant is 1/2 or 0.5.
For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.
Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.
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You bought 4 cakes to split between 7 teachers what fraction of a cake does each teacher get?
4/7
4 ÷ 7 = 4/7
fraction means division
a researcher states that he expects that there will be a significant difference between 20- and 30-year- olds after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance. what kind of hypothesis is being used in this study?
The kind of hypothesis is being used in this study is Research hypothesis
Hypothesis
In statistics, a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon is known as hypothesis.
Given,
Here we know that a researcher states that he expects that there will be a significant difference between 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.
And we need to find the kind of hypothesis is being used in this study.
While we looking into the given question we know that a researcher contacts the research on 20- and 30-year- old's after a 12-week exercise training program using exercise heart rates and myocardial oxygen consumption as measures of performance.
And her record the result accordingly.
Basically this one refers his research hypothesis.
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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
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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At the circus, the McCartney family bought bags of cotton candy and funnel cakes for. The Lennon family bought bags of cotton candy and funnel cakes for. Which system of equations could be used to find the cost of each item?
The system of equations which is used to find out the cost of each item (i.e cotton candy and funnel cake) bought by two families McCartney and Lennon Family is
3c + 2f = $24
2c + 4f = $32
We have given that
McCartney family bought
total number of bags of cotton = 3
total number of funnel cakes = 2
total cost of 3 bags and 2 funnel cakes is $24.
Lennon Family bought
total number of bags = 2
total number of funnel cake = 4
total cost of 2 bags and 4 funnel= $32
we have to find out the system of equations which used to find the cost of each item.
let the cost of each funnel cake be f and cotten candy be c .
then, using the above data we get
3c + 2f = $24 ---(1)
2c + 4f = $32 --(2)
Hence, equation (1) and (2) make a system of linear equations which is used to determine the cost of each item.
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Complete question:
HEME At the circus, the McCartney family bought 3 bags of cotton candy and 2 funnel cakes for $24. The Lennon Family bought 2 bags of cotton candy and 4 funnel cakes for $32. Which system of equations could be used to find the cost of each item? Let f represent funnel cake and c represent cotton candy
if the list price is $70 and the percent of discount is 10%. What is the amount of discount
Answer: 7
Step-by-step explanation: You would multiply 70 by 10 to get 700, then divide it by 100 to get 7. So, it would be 7 dollars.
Answer: 7
Step-by-step explanation:
Determine the coordinates of W(−7, 4) after a reflection in the line y=9
The coordinate of the reflection about the line y = 9 is thus (7, 4)
What is reflection?Reflection is a transformation in which an object is flipped over a line.
How to find the coordinates of W(−7, 4) after a reflection in the line y = 9?We know that to reflect W(-7, 4) over the line y = 9, the distance of the point W and its reflection from the line y = 9 must be the same.
The distance of point W(-7, 4) from the line y = 9 is d = 9 - (- 7) = 9 + 7 = 15
So, the x - coordinate of the reflection from the line y = 9 is x = 15 - 9 = 7
Since the y - coordinate of the point W, does not change, the coordinate of the reflection about the line y = 9 is thus (7, 4)
So, the coordinate of the reflection about the line y = 9 is thus (7, 4)
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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin xyzj + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Why do we use the line integral form of stokes theorem to integrate this, instead of the stokes variation that uses the curl?
We can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.
What is the Stokes' Theorem?According to Stoke's theorem, where C = A closed curve, "the surface integral of the curl of a function across a surface limited by a closed surface is equal to the line integral of the particular vector function over that surface."
S = Any surface bordered by C.
So, by utilizing Stokes Theorem to calculate S curl F .dS.
[tex]\iint_s c u r l F \cdot d s=\int_c F d r[/tex]
Parameterize C now.
r(t) = (3 cos t, 3 - 3 sin t)
When t is in [0 2].
Now,
[tex]\begin{aligned}& \int_c F \cdot d r=\int_0^{2 \pi} F(3 \cos t, 3-3 \sin t) \cdot r^{\prime}(t) d t \\& =\int_0^{2 \pi}\left(\left(9 \cos ^2 t\right)(27)(-3 \sin t),(\sin t) \times(-27 \cos t \cdot \sin t) \cdot(-3 \sin t, 0-3 \cos t) d t\right. \\& =27 \int_0^{2 \pi} 81 \cos ^2 t \cdot t \sin ^2 t+3 \cos ^2 t . t \sin t d t \\& =27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2 t+27\left[-\cos ^3 t\right]_0^{2 \pi}\end{aligned}[/tex]
[tex]\begin{aligned}& =27 \times \frac{81}{4} \int_0^{2 \pi}\left(\frac{1-\cos 4 t}{2}\right) \\& =\frac{2187}{8}\left[t-\frac{1}{4} \sin 4 t\right]_0^{2 \pi} \\& =\frac{2187}{8}\left[2 \pi-\frac{1}{4} \sin 4(2 \pi)-0-\frac{1}{4} \sin 4(0)\right] \\& =\frac{2187 \pi}{4}\end{aligned}[/tex]
Therefore, we can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.
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Erica recorded the number of sales she made during each of the first 4 months when
she began her new career. Erica plotted the data on a coordinate grid, and she noted
that the data correlate to an exponential equation, as shown.
What is the domain of the function shown in the graph?
The domain for the given graph is obtained as {1, 2, 3, 4}.
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
From the graph of the given exponential function,
The set of ordered pairs can be written as follows,
{(1, 10), (2, 20), (3, 40), (4, 80)}
Since the domain is the set of first elements for a given pair of ordered set.
The domain is given as {1, 2, 3, 4}.
Hence, the domain obtained from the given graph is {1, 2, 3, 4}.
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The graph missing in the question is attached here.
Drag the tiles to the correct boxes to complete the pairs.
Match the one-to-one functions with their inverse functions.
f(x)=-17
f(x)=x-10
Inverse Function
f-¹(x) = 5x
ƒ-¹ (x) = ²
f-¹ (z) = x + 10
f-¹ (z) = 3(z+17)
f(x) = √2x
Function
f(x) = //
The inverse of a function is f^-1(x) = 3(x + 17)/2 and f^-1(x) = x + 10
What is function ?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.
Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.
1.f(x) = 2x/3 - 17
Finding the inverse
y = f(x)
= 2x / 3 - 17
Exchange the variables, x for y and y for x
x = 2y / 3 - 17
Isolate the variable y
Adds 17 both sides
x + 17 = 2y / 3
Multiply by 3 both sides
3(x+17) = 2y
Divide by 2 both sides
y = 3(x + 17)/2
let f^-1(x) = y
f^-1(x) = 3(x + 17)/2
2. f(x) = x - 10
Finding the inverse
y = f(x)
= x - 10
Exchange the variables, x for y and y for x
x = y - 10
Isolate the variable y
Adds 10 both sides
y = x + 10
Multiply by 3 both sides
3(x+17) = 2y
let f^-1(x) = y
f^-1(x) = x + 10
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the sample mean is the point estimator of
the sample mean is the point estimator of μ
Sample Mean:
The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.
Point Estimate:
p=x/
p is the point estimate for the population proportion, x is the number of
successes, n is the sample size
p= + /2
for the population proportion
x= + /2
for the population mean
= − /2
is the margin of error
the sample mean is the point estimator of μ
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What is 2 divided by 3? Explain the steps pleas.
The value of 2 divided by 3 is 0.67
How to evaluate the quotient expression?From the question, we have the following parameters that can be used in our computation:
2 divided by 3
To start with, we need to represent the expression properly as a quotient
So, we have the following representation
2 divided by 3 = 2/3
Evaluate the quotient expression using a calculator
This gives
2 divided by 3 = 0.67
Hence, the solution to 2 divided by 3 is 0.67
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Which graph has a slope of 4/5?
Answer: Second graph from top.
Step-by-step explanation:
Slope is written in change in y over change in x. In other words, "rise over run" so the slope of 4/5 means rise 4 units and move 5 units right. The graph that meets this requirement is the second graph, as shown in the attachment.
You roll a 6- sided die what is p (greater than 3 or factor of 14)
Answer:
7
Step-by-step explanation:
piecewise linear functions common core algebra 2 homework answers
Piecewise linear functions, f(x) as common core algebra, Evaluate each of the following :
(1) f(-3) = 12
(2) f(4) = 2
(3) f(0)= 8
(4) f(3)= 8
What is Piecewise linear functions ?A piecewise linear function is a function defined on the interval [xₘᵢₙ ,xₘₐₓ]. A piecewise linear function is a function that consists of straight line segments. This is a piecewise function whose pieces are affine (linear) functions. Graphs of piecewise linear functions consist of line segments and rays.
We have given that,
f(x) = 5x - 3 ; x< -2
= x+8 ; -2≤x< 3
= 1/3(x) + 7 ; x ≥3
we see here that , f(x) is a piecewise linear function defined on interval [-2,3).
Now, we solve the following
(1) f(-3) , here x = -3< -2 i.e we take f(x) =5 x -3
=> f(-3) = 15 - 3 = 12
(2) f(4) , x= 4 >3 so, f(x) = 1/3(x) + 7
=> f(4) = 1/3(4) + 7 = 14/7 = 2
(3) f(3) , x = 3 so, f(x) = 1/3(x) + 7
=> f(3) = 1/3(3) + 7 = 8
(4) f(0) , x = 0 or -2 < x < 3 so, f(x) = x+8
=> f(0) = 0+8 = 8
Hence, we evaluate the given functions.
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Complete question:
piecewise linear functions common core algebra 2 homework answers
5x - 3 x<-2 1. For f (x) = x+8 -25x<3 answer the following questions. -x+7 x23 (a) Evaluate each of the following by carefully applying the correct formula: (1) f ( -3 ) (ii) f (4) (iii ) f ( 3 ) (iv ) f (0 )
elizabeth's family went to nyc for their vacation. at the gift shop on liberty island, valerie bought three t-shirts and four keychains for $134, and jennifer bought four t-shirts and five key chains for $175. find the price of each item.
Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.
In the given question, Elizabeth's family went to NYC for their vacation.
At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.
We have to find the price of each item.
Let the price of one t-shirt = $x
Let the price of one Key chain = $y
According to question
Price of three t-shirts and four key chains = $134
So the equation is
3x + 4y = $134……………….(1)
Also,
Price of four-shirts and five Key chains = $175
So the equation is
4x+5y = $175……………………..(2)
Now solving the equation using the elimination method.
Multiply Equation (1) by 5 and Equation (2) by 4, we get
15x+20y = 670....................(3)
16x+20y = 700......................(4)
Subtract equation 4 and 3, we get
x = 30
Now put the value of x in equation 1,
3*30 + 4y = $134
90+4y=$134
Subtract 90 on both side, we get;
4y = 44
Divide by 4 on both side, we get;
y = 11
Hence, the price of one t-shirt is $30 and one key-chain is $11.
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Select the values that make the inequalityt > -1 true.
(Numbers written in order from least to greatest going across.)
The values that make v ≥ 1 inequality true are 2, 3, 4, 5....
What is inequality in mathematics?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
The inequality is given as:
v ≥ -1
The values of c for which the given inequality → v ≥ -1 is true will belong to the set (say A) -
A = [-1, - ∞)
Therefore, we have to select all numbers which fall in this set. The numbers are
-1, 0, 1, 2, 3,....
Rewrite properly as:
v ≥ 1
The above means that the true values of v are values greater than 1.
Hence, the values that make v ≥ 1 inequality true are -1, 0, 1 , 2, 3, 4, 5....
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i've asked 55 students on monday whether they did their homework over the weekend. 17 of them said they did. find a 67% confidence interval for the proportion of students who will tell me that they did their homework over the weekend.
We are 67% confident that the proportion of students who are tell me that they did their homework over the weekend.0.087 with a margin of error of 0.0175
Find the confidence interval ?In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
87/1000 = 0.087
We have a 67% confidence level that the percentage of left-handed students is 0.087, with a 0.0175 margin of error.
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Which of the following choice are the factors of X² 5x 6?
Answer:
Step-by-step explanation:
Assuming that you mean x² + 5x + 6
the factors are (x + 2) and (x + 3).
Locate points A and B in the coordinate plane below. Use the Pythagorean Theorem to find the straight-line distance from each point to the origin.
Which point is close to the origin and by how much?
the options for the first one is "A" or "B" and the options for the second one is " more than" or "less than". (please ignore my chosen answer, I was just guessing.)
The coordinates of points A and B are (-4, 5) and (2, 6) respectively. Point B is close to the origin by 0.1 unit
How to locate points A and B in the coordinate plane?The positions or coordinates of points A and B are (-4, 5) and (2, 6) respectively
In order to use the Pythagorean Theorem to find the straight-line distance from each point to the origin (Consider the attached image):
Distance for point A
d = √((-4)²+5²)
d = √41 = 6.40 units
Distance for point A
d = √(2²+6²)
d = √40 = 6.32 units
To find which point is close to the origin and by how much:
The distance of B is less, so point B is close to the origin
Difference of distance = 6.40 - 6.32 = 0.08 ≈ 0.1 unit
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does there exist a polynomial time reduction from every problem in np-complete to every other problem in np-complete?
Yes, by definition, every NP problem can be reduced to an NP-complete problem in polynomial time.
All NP-complete problems can be reduced to each other in polynomial time since an NP-complete problem is itself an NP problem.
An NP-complete problem lies in NP, the set of all decision problems whose solutions can be verified in polynomial time. Similarly, NP can be defined as a set of decision problems that can be solved in polynomial time by a non-deterministic Turing machine. A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) to p in polynomial time.
Not sure if all NP issues can be resolved quickly. This is called the P-NP problem. However, if every NP-complete problem can be solved quickly, the definition of an NP-complete problem states that every problem in NP must be rapidly reducible to every NP-complete problem (i.e., it can be solved in polynomial time abbreviated by ). For this reason, NP-complete problems in general are often said to be harder or harder than NP problems.
A decision problem C is NP-complete if:
1. C is in NP and every problem in NP is reducible to C in polynomial time.
2. We can show that C is in NP by showing that the candidate solutions for C can be verified in polynomial time.
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a researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. how should we interpret the relationship between these variables?
In the above condition of positive correlation, the higher a person scores on involvement, the higher they tend to score on life satisfaction. Therefore, the option B holds true.
Positive correlation can be referred to or considered as the correlation, wherein the relationship between two or more elements, that are taken into consideration, is direct. The direct relationship means that the movement of a change in one element leads to an equal movement in the other. Positive correlation also states about the measure of life satisfaction in the above condition.
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Complete question
A researcher finds a positive correlation between a measure of community involvement and a measure of life satisfaction. How should we interpret the relationship between these variables?
A) There is no relationship between involvement and life satisfaction.
B) The higher a person scores on involvement, the higher they tend to score on life satisfaction.
C) The higher a person scores on involvement, the lower they tend to score on life satisfaction.
D) Involvement and life satisfaction are probably the same variable
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?
The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.
How to obtain the viable solutions?The variables for this problem are given as follows:
The input variable b represents the number of books ordered.The output variable w represents the total weights of the books, in ounces.To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.
Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.
Missing InformationThe table is given by the image shown at the end of the answer.
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Find the coordinates of the circumcenter of the triangle with the given vertices.
A(0, 0), B(0, 8), C(6, 0)
x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.
What is perpendicular in triangle?
The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.
The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.
A(0, 0), B(0, 8), C(6, 0)
Circumcenter , P(x,y)
AP = BP = CP
AP² = BP²
(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²
x² + y² + 64 - 16y = x² + y²
64 - 16y = 0
16y = 64
y = 4
BP = CP
BP² = CP²
(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²
x² + y² = x² 36 - 12x + y²
36 - 12x = 0
12x = 36
x = 3
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How do you simplify (−2−i)^2?
[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.
Multiply the integer by itself.
[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]
[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]
Simplify
[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]
[tex]=4+4i-1[/tex]
Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.
[tex]4+2i+21i+1(-1)[/tex]
Simplify and use the a+bi formula in standard form.
[tex]3+4i[/tex]
A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.
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HELP PLEASEJG
Problem: What is the actual distance between two cities if it is drawn to scale of 1:3,000,000 and it is 3 cm on the map?
Answer:
distance between two cities will be 9 000 000 km
Answer:
Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km
Which of the following is not a criterion for congruence of ∆ s a SAS B ASA C SSA D SSS?
(C) SSA is not a requirement for triangle congruence.
What is the congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
Right angle-hypotenuse-side (RHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
We know that SSA is not the criteria for the congruence of the triangles.
Therefore, (C) SSA is not a requirement for triangle congruence.
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a manufacturer must test that his bolts are 1.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.06cm. he knows that the population standard deviation is 0.22cm. assuming a level of significance of 0.10, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
p < 0.10, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.
In this question we have,
The population mean μ = 1.00
The sample size n = 49
The sample mean X = 1.06
The standard deviation σ = 0.22cm
The significance level α = 0.10
So, the hypothesis is:
The null hypothesis: H0: μ = 1
The alternative hypothesis: Ha: μ ≠ 1
Thus, the test statistic value is,
z = (X - μ)/(σ/√n)
= (1.06 - 1)/(0.22/√49)
= 0.06 / 0.03142
= 1.91
So, for z = 1.91, the p-value is 0.028067.
The provided significance level of 0.10 is not met by the p-value of (0.028067).
Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.
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