what the information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.5 level of significance? write out the hypothesis and explain the testing procedure in details
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Answer:
Check Explanation
Step-by-step explanation:
Complete Question
Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.
Solution
The information required to run an hypothesis test to compare the annual bonuses of employees at company A and employees at company B.
- First of, we require a sample of bonuses from each of the two firms, to calculate the mean bonus at each of the companies and the standard deviation.
- We also need the data to satisfy the conditions necessary for an hypothesis test.
the major conditions for an hypothesis test is that
1) The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.
2) The sample should be exrracted from a normal distribution population or approximate a normal distribution, so as to ensure almost normal behaviour from the samples
Then, to do the test,
Step 1
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this test, we want to investigate if the difference in annual bonuses for employees of company A and employees of company B is greater than $100.
Hence, the null hypothesis is that there is no sufficient evidence to suggest that the difference in annual bonuses for employees from company A and employees from company B is greater than $100.
And the alternative hypothesis is that there is sufficient evidence to suggest that the difference in annual bonuses for employees from company A and employees from company B is greater than $100.
Mathematically, if the difference in mean annual bonuses for employees from company A and employees from company B is μ
The null hypothesis is represented as
H₀: μ ≤ 100
The alternative hypothesis is represented as
Hₐ: μ > 100
Step 2
The testing procedure for this is a two-sample hypothesis test, Hence, we compute the test statistic in the next step.
Note that we must have had the mean of each of the samples (μ₁ and μ₂) and their standard deviations from the sample of annual bonuses of employees from both firms (s₁ and s₂)
Such that μ = μ₁ - μ₂
Test statistic = (μ - 100)/σₓ
σₓ = √[(s₁²/n₁) + (s₂²/n₂)]
Test statistic =
[(μ₁ - μ₂) - 100] ÷ √[(s₁²/n₁) + (s₂²/n₂)]
Step 3
Using the test statistic calculated, the significance level, the degree of freedom and the p-value table, we obtain the p-value.
Degree of freedom = n₁ + n₂ - 2
Step 4
The interpretation of p-values
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
Hope this Helps!!!
Related Questions
PLEASE HELP THE QUESTION IN THE PICTURE.
Answers
the answer is 4/5 this is know to be hard
A game has 19 more red cards than blue cards. The game has 43 red cards. How many blue cards does the game have?
Answers
Answer:
24
Step-by-step explanation:
43-19 =24
Please let me know if I am wrong.
Enter the number that belongs in the green box
Answers
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.
A: If no one has been cast yet, how many different ways are there to cast Fantine from the 28 women?
B: If Fantine has already been cast, how many different ways are there to cast adult Cosette from the remaining women?
C: If Fantine and adult Cosette have already been cast, how many different ways are there to cast Éponine from the remaining women?
Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.
B: 27P2
C: 26
C: 26!
A: 28P3
B: 27
C: 26P1
A: 28
B: 27!
A: 28!
Question 2:
A: Which of the following expressions will calculate the number of ways the three lead female roles could be cast?
B: Evaluate the permutation from part A.
Select one answer choice for part A, and one answer choice for part B.
B: ≈3.05×10^29
A: 28P3
B: 19656
A: 3P28
B: ≈5.08×10^28
A: 28P25
Answers
The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.
How to calculate the value?The different ways that are there to cast Fantine from the 28 women will be:
= 28!/(28 - 1)!
= 28!/27!
= 28
When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:
= 27!(27 - 1)!
= 27!/26!
= 26
When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:
= (28 - 2)!/(28 - 2 - 1)!
= 26!/25!
= 25
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a college official conducted a survey to estimate the proportion of students currently living in dormitories about their preference for single rooms, double rooms, or multiple (more than two people) rooms in the dormitories on campus. which of the following does not affect the college official's ability to generalize the survey results to all dormitory students?
Answers
The correct answer is Option (b) i.e; the survey was sent only to first year students as it represents a particular subset of the population.
Given that,
A college official conducted a survey to estimate the proportion of students currently living in dormitories about their preference for single rooms, double rooms, or multiple (more than two people) rooms in the dormitories on campus.
To find : Which of the following does not affect the college official's ability to generalize the survey results to all dormitory students
(a) Five thousand students live in dormitories on campus. A simple random sample of only 500 were sent the survey.
(b) The survey was sent only to first year students.
(c) Of the 500 students who were sent the survey, only 160 responded.
(d) All of the above present a problem for generalizing the results.
In option (B), it reflects the college official's ability to generate and generalize the survey results. As it does not interfere with the college official's capacity to apply the survey results to all students living in dormitories.
Therefore, option (b) is the right answer.
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> Next question
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 4 and a root of multiplicity 1 at
x = - 1. The y-intercept is y = -6.4.
Find a formula for P(x).
P(x) =
Answers
P(x) = -.4x^3 +2.8x^2 -3.2x -6.4 is the 3rd degree polynomial with the given roots and y intercept.
What is polynomials?
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.P(x) = a(x+1)(x-4)^2
= a(x+1)(x^2 - 8x + 16)
= a(x^3 -7x^2 +8x +16)
=a(x^3 -7x^2 + 8x) + 16a
where 16a = -6.4,
a = -6.4/16
a = -.4
P(x) = -.4(x^3 -7x^2 + 8x + 16)
P(x) = -.4x^3 +2.8x^2 -3.2x -6.4 is the 3rd degree polynomial with the given roots and y intercept .
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Demand will decrease shift when …
Answers
Answer:Cuando, al precio corriente, la demanda excede la oferta, aumenta el precio. Inversamente,
Step-by-step explanation:
cuando la oferta excede la demanda, disminuye el precio. Un aumento en el precio disminuye, más tarde o más temprano, la demanda y aumenta la oferta.
Precalculus question:
A polynomial f(x) and one or more of its zeros are given. (pictured below)
a) Find all the zeros. Write in the exact simplest form.
b) Factor f(x) as a product of linear factors
c) Solve the equation f(x)=0
Answers
Considering the polynomial f(x) = x^4 - 16x³ + 70x² + 48x - 219, we have that:
a) The zeros are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.
b) The linear factors are: (x + 1.995)(x - 1.995)(x - 8 + 3i)(x - 8 - 3i).
c) The solutions to f(x) = 0 are: x = -1.995, x = 1.995, x = 8 - 3i, x = 8 + 3i.
How to obtain the zeros of the polynomial?The given zero of the polynomial is:
8 + 3i
Hence it's conjugate is also a zero, that is:
8 - 3i.
Thus the first two factors are given as follows:
(x - 8 - 3i)(x - 8 + 3i) = x² - 16x + 64 + 9i² = x² - 16x + 55.
Then the polynomial can be written as follows:
x^4 - 16x³ + 70x² + 48x - 219 = (ax² + bx + c)(x² - 16x + 55).
As a fourth order polynomial can be the product of two second order polynomials. Applying the distributive property to the right side of the equality, we have that:
x^4 - 16x³ + 70x² + 48x - 219 = ax^4 + x³(b - 16a) + x²(55a + c - 16b) + x(55b - 16c) + 55c.
Then the coefficients are given as follows:
a = 1.55c = -219 -> c = -219/55 -> c = -3.98.b - 16a = -16 -> b = 0.Hence the other two factors are given as follows:
x² - 3.98 = 0
x = ± sqrt(3.98)
x = ± 1.995.
The linear factors are:
(x - x')(x - x'')(x - x''')(x - x'''').
In which x', x'', x''' and x'''' are the roots.
The solutions to f(x) = 0 are the roots.
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please help due tomorrow
Answers
Answer:
1) v= -3, -5
2) n= 3, -1
3) i don't see a solution so- no solution
4) m= -11/5, 5 or -2 1/2, 5
5) k= 13, 8
6) b= 3.53867
7) ????
8) ????
9) n= -4, -6
10) m= 1.78233
11) x= 2/3, -1
12) x= 1, 0.2(1/5)
13) a= -1/3, 4/3
14) b= -3/7, -8
15) b= 2, -3
16) x= 4, -2
im way too lazy to put in my work. sorry.
50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! PLEASE HELP
Which scatterplot(s) show a positive linear association between the variables?
A.
Table A only
B.
Neither table
C.
Table B only
D.
Both tables
Answers
Answer:
Step-by-step explanation:
I'd say c.) table b only. Because it's a straight line which I think is positive but i'm not sure about the association between the variables part. If wrong I'm sorry.
Please help me with my homework!!!!
Answers
Answer:
-3.5
Step-by-step explanation:
Flip the equation so it's 0 - 3.5 which would give you -3.5
Answer:
- 3 \(\frac{1}{2}\)
Step-by-step explanation:
Any number combined with it's opposite will make zero. The opposite of a number is the same number with it's sign flipped. For example, the opposite of 5 is -5, and the opposite of -3 is 3. If I combine any number, for example 10, with it's opposite, in this case -10, it will make zero. (10 - 10 = 0.) Hope this helps!
If 15% of the customers total is $98,880, then the sum total equals what
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The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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The cost for a 7-day business trip for 4 people is $1,833 per person. The cost per person includes
flight, hotel, food, and spending money. The business trip would use 78% of the company's travel
budget. Find the total amount of money the company has budgeted for travel. The total travel budget for the company is $?
Answers
Answer:
9400 lol I hope its right but I'm not sure how I got it tho i hope it help
IF M
PLEASE EXPLAIN ??
Answers
Select all numbers that have an absolute value of 4.
Answers
math math math math math
Answers
The measure of angle QOB is 90° and the measure of angle COZ is 150°
What is angle on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.
The sum of angles on a straight line is 180°
since angle LOB = 150° and line OB is perpendicular to line OQ
Therefore the angle between perpendicular lines is 90°. This means that angle QOB = 90°
Since LOB = 150°,
LOQ = 150-90 = 60°
Since OC is the bisector of angle LOQ,
COQ = 60/2 = 30°
Therefore angle COZ = 30+ 90+30
= 150°
the measure of angle COZ is 150°
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Answer: The measure of angle QOB is 90° and the measure of angle COZ is 150°
Step-by-step explanation:
What is the value of x when the Richter
scale rating is 4.37 Round your answer
to the nearest hundredth.
Answers
Step by step explanation:
It’s correct on Plato
Arătati ca numărul ab1 + a1b + 1ab
Answers
Answer:
a plus b equals 9923
Step-by-step explanation:
Bakit mahalaga humingi ng tulong sa iba?
Answers
Answer: Ang paghanap ng tulong ay binabawasan ang gastos at epekto ng sakit at pinapayagan ang maraming tao na umunlad at umunlad at mag-ambag sa isang mas positibong lipunan. Ang paghanap ng tulong ay dapat, makita, bilang isang positibong hakbang; isa na nagpapabuti sa kalusugan at kabutihan at kaligayahan.
Step-by-step explanation: Pinoy ka? Ako den
Answer:
ayon sa internet, "ang paghingi ng tulong ay binabawasan ang gastos at epekto ng karamdaman at pinapayagan ang mas maraming tao na umunlad at umunlad at mag-ambag sa isang mas positibong lipunan." Sa madaling salita, ang paghihingi ng tulong ay maaaring payagan kang mapalibutan ang iyong sarili sa mga tao na maaaring magpaganda sa amin.
(gumamit ako ng tagasalin. pasensya na kung hindi mo maintindihan!) :(
Step-by-step explanation:
For a Saturday matinee, adult tickets cost $8.50 and kids under 12 pay only $7.00. If 80 tickets are sold for a total
of $605, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answers
Answer:
30 adult tickets,50 kids ticketsStep-by-step explanation:
Given
Cost of adult ticket = $8.50Cost of kids ticket = $7.00Number of tickets = 80Total cost = $605Let the adult ticket be a and kids be k
We got equations
a + k = 808.5a + 7k = 605From the first equation we get
k = 80 -aSubstituting k in the second equation
8.5a + 7(80 - a) = 6058.5a - 7a + 560= 6051.5a = 45a = 45/1.5a = 30Then finding k
k = 80 - 30 = 50
A type of green paint is made by mixing 2 cups of yellow with 35 cups of blue.
1. Find a mixture that will make the same shade of green but a smaller amount
2. Find a mixture that will make the same shade of green but a large amount
3. Find a mixture that will make a different shade of green that is bluer.
4. Find a mixture that will make a different shade of green that is more yellow.
Answers
Answer:
1. 1 cup of yellow 17.5 cups of blue 2. 4 cups of yellow 70 cups of blue
3. 2 cups of yellow 40 cups of blue 4. 2 cups of yellow 30 cups of blue
Step-by-step explanation:
1. to get same shade keep ratios the same but divide by 2 for smaller amount
2/2 = 1 and 35 /2 = 17.5
2. similar to 1. except multiply by 2
3. use same yellow amount but more blue
4. use same yellow but less blue
the price of a gallon of gas dropped from 3.50 to 2.87 by what percentage was the price gas reduced
Answers
Answer:
18%Step-by-step explanation:
To do this, we first divide 2.87 by 3.50. This gets us 0.82. So we now know that 2.87 is 82% of 3.50. But we're trying to find the reduced amount. So we now Do 100%-82% (82% being 2.87) to get 18%. So the answer is 18%. To make sure we are right, we do 18% of 3.50 to get 0.63 cents. We then take 3.50 and subtract 0.63 to get 2.87. So it reduced by 18%
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.
How should you construct the first statement in a proof?When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.
It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.
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Answer please. Tysm!
Answers
Answer:
6a5 + 5b
Step-by-step explanation:
Please someone help me
Answers
Answer:
B) 1/9
Step-by-step explanation:
There are nine squares. One of them has double pepperoni (PP).
1/9
can someone help me on this question with step by step explaination
and reasoning
Answers
Answer: Same
Step-by-step explanation:
Given formula
\(Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%\)
Given information
Troop A:
Original (2010) = 14New (2011) = 16Troop B:
Original (2010) = 21New (2011) = 24Substitute values into the formula (Troop A)
\(Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%\)
\(Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%\)
Simplify the fraction
\(Percent~of~change~=~\Large\frac{2}{14}*100\%\)
\(Percent~of~change~=~\Large\frac{1}{7}*100\%\)
\(Percent~of~change~\approx~14.29\%\)
Substitute values into the formula (Troop B)
\(Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%\)
\(Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%\)
Simplify the fraction
\(Percent~of~change~=~\Large\frac{3}{21}*100\%\)
\(Percent~of~change~=~\Large\frac{1}{7}*100\%\)
\(Percent~of~change~\approx~14.29\%\)
Compare the two percent of change
\(Troop~A~v.s.~Troop~B\)
\(14.29\%~=~14.29\%\)
Therefore, they are \(\Large\boxed{Same}\)
Hope this helps!! :)
Please let me know if you have any questions
The answer is same.
Finding the percentage of change for Troop A :
New - Original / Original × 100%
16 - 14 / 14 × 100%1/7 × 100%14.29%Finding the percentage of change for Troop B :
24 - 21 / 21 × 100%1/7 × 100%14.29%Both the troops have the same percent change in membership.
What is the answer? Thank u
Answers
Answer:
21.45 ft (nearest hundredth)
Step-by-step explanation:
Let P be the spot where the basketball player is standing, B be the base of the hoop and H be the top of the high hoop.
Please see the attached picture for the full solution.
Triangle ABC = Triangle ADF, AD = 18, BC = 17, DF= [?]
![Triangle ABC = Triangle ADF, AD = 18, BC = 17, DF= [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/5vv3ZE9SDhOBDlaQtAto8j3QTu9kKrP0.png)
Answers
The value of the length DF is 17
How to determine the length DF?The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.
So, we have:
AB = AD
AC = A F
BC = DF
Given that BC = 17;
The equation BC = DF becomes
17 = DF
Rewrite as:
DF = 17
Hence, the value of the length DF is 17
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Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answers
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
What are the points of the image of the line in Q4 after the dilation?
Answers
Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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