The mean hourly wage for employees in industries is currently $24.57. Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the U.S industries. a. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the U.S industries. b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. c. With α = .05 as the level of significance, what is your conclusion? d. Repeat the preceding hypothesis test using the critical value approach.
Answers
Answer:
(a) Null Hypothesis, \(H_0\) : \(\mu\) = $24.57
Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) $24.57
(b) The P-value of the test statistics is 0.1212.
(c) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using P-value approach.
(d) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using critical value approach.
Step-by-step explanation:
We are given that a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the U.S industries.
Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour.
Let \(\mu\) = population mean hourly wage in the manufacturing industry.
(a) Null Hypothesis, \(H_0\) : \(\mu\) = $24.57 {means that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries}
Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) $24.57 {means that the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the U.S industries}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) ~ N(0,1)
where, \(\bar X\) = sample mean wage in the manufacturing industry = $23.89/hr
σ = population standard deviation = $2.40/hr
n = sample of employees from the manufacturing industry = 30
So, the test statistics = \(\frac{23.89-24.57}{\frac{2.40}{\sqrt{30} } }\)
= -1.55
The value of z test statistics is -1.55.
(b) Now, the P-value of the test statistics is given by;
P-value = P(Z < -1.55) = 1 - P(Z \(\leq\) 1.55)
= 1 - 0.9394 = 0.0606
For two-tailed test P-value is calculated as = 0.0606 \(\times\) 2 = 0.1212
Since, the P-value of the test statistics is higher than the level of significance as 0.1212 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.
(d) Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.
Related Questions
Use technology to find points and then graph the line y=-5(x-5)+1, following the instructions below.
Answers
According to the given question, we are to plot the graph of the line y= -5(x-5)+1. To do that, we will first create coordinate points on the plane in the form of (x, y)
If y = 10, then;
10 = -5(x-5) + 1
10-1 = -5(x-5)
9 = -5(x - 5)
x- 5 = -9/5
x - 5 = -1.8
x = -1.8 + 5
x = 3.2
Hence one of the coordinates that fit is ABB(3.2, 10)
If y = 5, then;
5 = -5(x-5) + 1
5 - 1 = -5(x - 5)
4 = -5(x - 5)
x - 5 = -4/5
x - 5 = -0.8
x = -0.8 + 5
x = 4.2
Another coordinate point that fit into the plane is B(4.2, 5)
The required graph is as plotted below;
just explain how this is "Reflexive Property" (30 points)!!
Answers
The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.
In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.
So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.
A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3
Answers
Answer:
108 cube
Step-by-step explanation:
the volume of one cube is (1/3)^3 = 1 / 27
1/27X = 4
X = 108
Planes A and B are shown.
m
n
B
MA
If a new line, p, is drawn parallel to line /, which
statement is true?
O
Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line /
O Line p must be drawn in the same plane as line n.
Answers
The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, so option C is correct.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
The given planes are A and B,
A new line, p, is drawn parallel to line l,
Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.
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The image of the remaining question is attached below.
With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
Answers
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
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an aquarium at a pet store, holds 3 gallons of water. how many aquariums will it take to hold 10 gallons?
Answers
Answer:
you will need 30 aquariums to hold 10 gallons.
Step-by-step explanation:
3.10=30
10/3 aquariums will it take to hold 10 gallons.
What is unit rate?Unit rate is defined as the ratio of two quantities used to find the amount associated with per unit of quantity.
Given that, an aquarium, holds 3 gallons of water, we need to find the number of aquariums will it take to hold 10 gallons,
So, 1 aquarium = 3 gallons
So, 1 gallon = 1/3 aquariums
So, 10 gallons = 10/3 aquariums
Hence, 10/3 aquariums will it take to hold 10 gallons.
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Is 7-¹ a negative number? Explain.
Answers
Answer:
No
Step-by-step explanation:
\(7^{-1}\) is a fraction
using the rule of exponents
• \(a^{-m}\) = \(\frac{1}{a^{m} }\)
then
\(7^{-1}\) = \(\frac{1}{7^{1} }\) = \(\frac{1}{7}\) ← that is a fraction
8. In the following diagram, the diameter of the circle is 15m. What is the distance between the chord and the edge of the circle?
Answers
Answer:
7
Step-by-step explanation:
15-8
a number b minus 4.2 is less than -7.5.
Answers
Answer:
B-4.2<-7.5
Step-by-step explanation:
Reflect the given triangle over
the y-axis.
3 6 31
-3 3 3.
{
ER
-3 -6
-3 [?] [
![Reflect the given triangle overthe y-axis.3 6 31-3 3 3.{ER-3 -6-3 [?] [](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/OWtEpLX1jVirGTwm06qPL96fpfvyOJDg.png)
Answers
Answer:
see explanation
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y )
applying this rule to the given points , then we obtain
\(\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\\\end{array}\right]\)
HELP I WILL GIVE BRAINLIEST IF RIGHT
Answers
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
I might be wrong but i'm pretty sure it's right
Question 10(Multiple Choice Worth 1 points)
(02.04 MC)
Write an equation of a line that is perpendicular to y = 6x + 3 that passes through (-6, 4).
Answers
Answer:
Step-by-step explanation:
equation perpendicular to y = 6x + 3 is y = (-1/6)x + k
the line passes through (-6,4)
putting the value we get, 4 = 1 + k
k = 3
So equation is y = (-1/6)x + 3
Question 3 of 5
At the fair, Jamal bought a cone-shaped ice treat. The cone was 10 inches tall and 10 inches in diameter. What was the volume of the
cone?
Answers
pi x radius squared x height
----------------------------------------
3
you need to find the radius which is half the diameter, so 5 inches
the height is given, 10 inches
sub the values into the formula
π x r^2 x h
--------------
3
π x 5^2 x 10
= -----------------
3
= 261.8 inches cubed (to 1 dp)
expressions that are equivalent to 8.8.8.8 8
Answers
Answer:
8.8
Step-by-step explanation:
This is the correct answer because the 8 repeats.
Old Navy has a sale on $15 shirts: buy 3
and get 40% off. How much would 3
shirts cost on sale?
Answers
The amount that the would be paid after 40% discount is $27
Word ProblemGiven Data
Cost of a shirt = $15Discount = 40%Let us find the cost of three shirt
= 15*3
= $45
Let us find 40% discount of $45
= 40/100*45
= 0.4*45
= $18
Let us find the amount after discount
= 45-18
= $27
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Perimeter = 16x + 8
The length of the indicated side is
Answers
Answer:
d
Step-by-step explanation:
Because you need to substitute the variable first, multiply that and add 8.
Question 12 of 22
Select the action you would use to solve = 16. Then select the property that
justifies that action.
A. Property: Multiplication property of equality.
B. Action: Add 4 to both sides.
C. Property: Addition property of equality.
D. Action: Divide both sides by 4.
E. Property: Division property of equality.
OF Action: Multiply both sides by 4.
Answers
Answer:
The correct answer is:
D. Action: Divide both sides by 4.
E. Property: Division property of equality.
Use calculus to find the area A of the triangle with the given vertices. (0, 6), (2, −3), (3, 4)
Answers
The area of the triangle with the given vertices is 11.5 square units.
Define the area of triangle by vertices?The area of a triangle can be calculated using the coordinates of its vertices using the following formula.
To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:
A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2
Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:
A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2
A = (0 - 4 + 27)/2
A = 23/2
A = 11.5
Therefore, the area of the triangle with the given vertices is 11.5 square units.
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06.07 equivalent expressions module six project 1 part2
Answers
Answer:
go to utube.com/RyStone and sub he has the answers
Step-by-step explanation:
Hes op
A student ran a distance of 312 miles each day for 5 days. Then the student ran a distance of 414 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
Answers
The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi
What is the total distance that the student ran on the 10 days?We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:
5*(3 + 1/2) mi = (15 + 5/2) mi
Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:
5*(4 + 1/4) mi = (20 + 5/4)mi
Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:
(15 + 5/2) mi + (20 + 5/4)mi
So we have a sum of mixed numbers, we can rewrite this as:
(15 + 5/2) mi + (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi
(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi
35mi + (10/4 + 5/4) mi = 35mi + 15/4mi
35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi
35mi + 12/4 mi + 3/4 mi = (38 + 3/4)mi
That is the total distance that the student ran on the 10 days.
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HELP ASAP!!! ILL GIVE BRAINLIEST!
The residents of a city voted on whether to raise property taxes. The ratio of YES votes to NO votes was 2 to 3. If there were 4735 TOTAL votes, how many NO votes were there?
Answers
Answer:
2841 no votes
Step-by-step explanation:
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
Answers
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem:
\(Z = \frac{X - \mu}{s}\)
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
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Find the surface area of a rectangular prism.
A rectangular prism with length 34 feet, width 21 feet, and height 10 feet.
a.
7140 sq. ft
b.
2528 sq. ft
c.
1264 sq. ft
d.
1814 sq. ft
Answers
Answer:
b.
2528 sq. ft
Step-by-step explanation:
Surface area of rectangular prism:
A rectangular prism has length l, width w and height h. It's surface area is given by:
\(S = 2(lw + lh + wh)\)
In this question:
We have that \(l = 34, w = 21, h = 10\)
So the surface area is
\(S = 2(lw + lh + wh) = 2*(34*21 + 34*10 + 21*10) = 2528\)
2528 square feet, option b.
Answer:
B.) 2528 Sq. Ft.
Step-by-step explanation:
Edge 2021
3x^2/3 - 2x^1/3 - 1 = 0
Answers
Answer:
x=1
Step-by-step explanation:
which ONE DOES NOT BELONG? 5231+4331=9462 or 3696+6936=10 635 or 1842+1614=3456 or 2184+4182=6996
Answers
Answer:
5231+4331=946 doesn't belong
Step-by-step explanation:
5231+4331=9562
What is another name for Angle 2? Lines E H and D F intersect at point G. Angle 2 is formed by line segments D G and G E and angle 1 is formed by line segments E G and G F. Angle D G E Angle G E D Angle E G F Angle G E F
Answers
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is A.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The diagram for the given problem can be made as shown below. Therefore, the other name for angle 2 will be ∠DGE.
Hence, the correct option is A.
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Answer:
a
Step-by-step explanation:
got it right
If a loading ramp is placed next to a truck, at a height of 8
feet, and the inclined portion of the ramp is 17 feet long, what angle (in degrees) does the ramp make with the ground?
Round your answer to one-tenth of a degree.
Answers
The angle that the ramp makes with the ground is approximately 28.07 degrees.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):
Sin(θ) = 8/17
We can use a calculator to find the inverse sin of this ratio to get the angle θ:
θ = sin⁻¹(8/17)
θ ≈ 28.07 degrees
Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.
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Please help me in this
Answers
Answer:
top=170mm squared
shape 2=76.27 cm squared
shape 3=62.862 cm squared
Step-by-step explanation:
top shape...
(18x15)-4(5x5)=area
270-4(25)=area
270-100=area
170=area
shape 2...
diameter of circle is 6 so radius is 3...
area=pier^2
a=28.27 and their are two half circles so that makes one whole circle
(8x6)+28.27=76.27 cm squared
shape 3...
total of rectangle with a half circle subtracted. r=4 d=8
so
11x8=88 for rectangle then subtract half circle
a=pie r^2
a=50.27
50.27/2=25.135 subtract this from rectangle total...
88-25.135=62.862 cm squared
12 - 1/5r = 2r + 1+??
Answers
Answer:
Step-by-step explanation:
Solve the equationSolve for rr=5Show Solutions Rewrite the equationRewrite in rectangular formx2+y2−25=0Show Solutions Graph
<1 and <5 are ___ angles.
right
vertical
alternate interior
corresponding
angles.
Answers
Answer:
corresponding
Step-by-step explanation:
<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m