Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
The populations are normally distributed. Determine the:
Hypothesis in symbolic form?
Determine the value of the test statistic?
Find the critical value or value?
determine if you should reject null hypothesis or fail to reject?
write a conclusion addressing the original claim?
Answer:
Step-by-step explanation:
GIven that :
Company A
Sample size n₁ = 16 workers
Mean [tex]\mu[/tex]₁ = 5.2
Standard deviation [tex]\sigma[/tex]₁ = 1.1
Company B
Sample size n₂ = 21 workers
Mean [tex]\mu[/tex]₂ = 4.6
Standard deviation [tex]\mu[/tex]₂ = 4.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu _1 = \mu_2[/tex]
[tex]H_1 : \mu _1 > \mu_2[/tex]
The value of the test statistics can be determined by using the formula:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
where;
[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]
[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]
[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]
[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]
[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]
[tex]\sigma p^2= 12.61[/tex]
Recall:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]
[tex]t = \dfrac{0.6}{1.178388981}[/tex]
t = 0.50917
degree of freedom df = ( n₁ + n₂ - 2 )
degree of freedom df = (16 + 21 - 2)
degree of freedom df = 35
Using Level of significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35
p - value = 0.3069
The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895
Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.
Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is no sufficient information that the claim that company a retains it workers longer than more than company b.
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5
True or false
Answer:
THE ANSWER WOULD BE TRUE MY FRIEND
Tom finished reading 3/7 of a book in the first week, and he read 3/4 of the remainder in the second week. what fraction is left?
Answer:
1/7 is left
Step-by-step explanation:
What is left to read after the first week
1 - 3/7
7/7 - 3/7
4/7
He read 3/4 of this the second week
4/7 * 3/4
3/7 was read
4/7 - 3/7 is what is left
1/7 is left
Answer:
The correct answer is
Step-by-step explanation:
1/7 of the book is left to read.
Hope this helps....
Have a nice day!!!!
please help :) Write the number shown in standard notation. 6.94 x 10 to the 6 power A. 694 B. 6,940,000 C. 694,000,000 D. 694,000
Answer:
B. 6,940,000
Step-by-step explanation:
6.94 x 10^6
Make the number "6.94" as 694.
Since we make this decimal point move 2 places to the right.
We should decrease 2 powers from 10^6
=> 694 x 10^4
=> 694 x 10000
=> 6,940,000
So, the answer is B
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
Answer:
Ok, our function is:
f(x) = 3*(x - 1)^2 + 2.
First, domain:
We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.
In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)
Then the domain is the set of all real numers.
Vertex:
Let's expand our function:
f(x) = 3*x^2 - 3*2*x + 1 + 2
f(x) = 3*x^2 -6*x + 2
The vertex of a quadratic function:
a*x^2 + b*x + c is at:
x = -b/2a
here we have:
a = 3 and b = -6
x = 6/2*3 = 6/6 = 1.
And the value of y at that point is:
f(1) = 3*(1 - 1)^2 + 2 = 2
Then the vertex is at: (1, 2)
Range:
The range is the set of all the possible values of y.
Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.
Then the minimal value of our quadratic function is the value at the vertex, y = 2.
This means that the range can be written as:
R = y ≥ 2
So the range is the set of all real numbers that are larger or equal than 2.
Which phrase best describes the relationship indicates by the scatter plotting?
Answer: negative correlation
Step-by-step explanation: If you look at the points in this graph here, I would say that those points are very close to a perfect line.
Notice that the slope of the line is negative.
This means it will be a negative correlation.
So the line is a very good estimate of the points.
Please answer now question
Answer:
1664 yd²Step-by-step explanation:
P = 2•(¹/₂•24•16) + 2•(20•20) + 24•20 = 384 + 800 + 480 = 1664 yd²
please help me for the homework
Answer:
refer to the pic attached
Please help me understand this number sequence
Answer:
Step-by-step explanation:
A=a(r)^t
a=1
time=2.5 hours=25/10 ×60=150 minutes
10t=150
t=150/10=15
[tex]A=1(2)^{15}=32,768[/tex]
5 times the quantity 7 minus a number f in an algebraic expression.
Answer:
(5*7)-f
Step-by-step explanation:
Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]
Algebraic expressionAlgebraic expression is the combination of terms that consists of numbers and variables connected by arithmetic operators.
Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.
We need to write it in an algebraic expression
5 times a quantity. for product we use multiplication sign
For addition we use + sign and for difference we use minus sign .
5 times the quantity 7 means 5 multiplied by 7
[tex]5 \cdot 7[/tex]
5 times the quantity 7 minus a number f
subtract f from the expression we got
[tex]5 \cdot 7 -f[/tex]
Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]
Learn more information about 'Algebraic expression ' here:
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5/14, 7/10, 5/6, 11/15, 19/2
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)− 6 1 ×(− 7 9 )minus, start fraction, 1, divided by, 6, end fraction, times, left parenthesis, minus, start fraction, 9, divided by, 7, end fraction, right parenthesis
Answer:
[tex]\dfrac{3}{14}[/tex]
Step-by-step explanation:
The even number of minus signs means the product will be positive. A factor of 3 can be removed to simplify the product. As usual, the numerator of the product is the product of numerators, and the denominator of the product is the product of denominators.
[tex]-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)=\dfrac{1\cdot 9}{6\cdot 7}=\dfrac{3\cdot 3}{3\cdot 14}=\boxed{\dfrac{3}{14}}[/tex]
Answer:
→ 3/4 ←
-1/6 × (-9/7)= 1·9/6·7 3·3/3·14 = 3/4
Help please on this question. I’d appreciate it if you answered.
Ok so the letters overwrap all of the alphabets and the other terms are in.
Answer:
see below
Step-by-step explanation:
Consonants and vowels do not overlap
There are no consonants that are vowels and no vowels that are consonants
That means the circles will never touch
Get this correct i will give u brainliest.
Answer:
x = - 2, y = - 8
Step-by-step explanation:
Given the 2 equations
13x - 6y = 22 → (1)
x = y + 6 → (2)
Substitute x = y + 6 into (1)
13(y + 6) - 6y = 22 ← distribute and simplify left side
13y + 78 - 6y = 22
7y + 78 = 22 ( subtract 78 from both sides )
7y = - 56 ( divide both sides by 7 )
y = - 8
Substitute y = - 8 into (2) and evaluate for x
x = - 8 + 6 = - 2
Thus x = - 2, y = - 8
After taking off from the landing pad, a helicopter flies 3 miles west, then 2 miles southeast. How far is the helicopter from the landing pad? If someone could explain to that would be very helpful
Answer:
When the plane makes its turn to fly southeast, it makes a 45º angle at point a, making angle abc also equal to 45º.
Line ab is the 2 miles southeast the plane flies.
Line ac = line cb
sine (45º) = opposite / hypotenuse = cb / 2
.70711 = cb / 2
cb = 1.41422 miles = line ac
Line cs = 3 - 1.41422 = 1.58578
Line x^2 = cs^2 + cb^2
Line x^2 = 2.5146982084 + 2.0000182084
Line x^2 = 4.5147
Line x = 2.1248
Step-by-step explanation:
what is the value of -19- (-18)?
Answer:
-1 is the answer
Step-by-step explanation:
I can't do the explanation of this question
Answer:
-1
Step-by-step explanation:-19 + 18 is basically how it is they end up canceling each other out except for the -1 which is the answer.
Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
Which expression represents the prime factorization of 243?
Answer:
[tex]\boxed{3^5}[/tex]
Step-by-step explanation:
Hey there!
Look at the image below↓
By looking at the image we can tell the PR expression is [tex]3^5[/tex].
Hope this helps :)
Answer:
Below in bold.
Step-by-step explanation:
Dividing by primes:
3 ) 243
3 ) 81
3 ) 27
3) 9
3.
So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.
Solve for x.
13(x-3) = 39
x=1
x=4
x=6
x= 10
Answer:
x=6
Step-by-step explanation:
13(x-3) = 39
Divide each side by 13
13/13(x-3) = 39/13
x-3 = 3
Add 3 to each side
x-3+3 = 3+3
x = 6
Answer:
x=6 ,is right.
6-3=3&multiply 13=39
so answer is x=6
mark brainleast plz
#5 Find the distance between the points on the graph.
Answer:
approximately 12.04 units
Step-by-step explanation:
We'll use the Pythagorean Theorem to solve this problem.
There are two points here. The horizontal distance between them is 8 units and the vertical distance is 9.
According to the Pythagorean Theorem (or the Distance Formula), the distance between the two points is
d = √(8^2 + 9^2) = √(64 + 81) = √145 units, or approximately 12.04 units.
Suppose that the cost of renting a snowmobile is $37.50 for 5 hours.
a. If c represents the cost and ݄ represents the hours, which variable is the dependent variable?
b. What would be the cost of renting 2 snowmobiles for 5 hours? please and thanks ( i"ll give brainiest )
Function g can be thought of as a scaled version of f(x)=|x| what is the equation for g(x)?
Answer:
A
Step-by-step explanation:
Khan academy
The equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| option (B) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Function g can be thought of as a scaled version of f(x)=|x|
The function f(x):
f(x) = |x|
The blue lines represent the function f(x)
First reflect the function f(x) around the x-axis
F(x) = -|x|
Multiply by the factor 4 to stretch the function:
g(x) = -4|x|
Thus, the equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| option (B) is correct.
Learn more about the function here:
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#SPJ5
4 - Q = -2 what is Q
Answer:
Q = 6
Step-by-step explanation:
Step 1: Write equation
4 - Q = -2
Step 2: Subtract 4 on both sides (Subtraction Equality)
-Q = -6
Step 3: Divide -1 on both sides (Division Equality)
Q = 6
And we have our answer!
Answer:
[tex] \boxed{Q = 6}[/tex]Step-by-step explanation:
[tex] \mathrm{4 - Q = - 2}[/tex]
Move constant to R.H.S and change its sign
[tex] \mathrm{ - Q = - 2 - 4}[/tex]
Calculate
[tex] \mathrm{ - Q = - 6}[/tex]
Change the signs on both sides of the equation
[tex] \mathrm{Q = 6}[/tex]
Hope I helped!
Best regards!
What is the measure of angle B?
Answer:
b = 60
Step-by-step explanation:
The sum of the angles of a triangle are 180
80+40+b = 180
Combine like terms
120+b =180
Subtract 120 from each side
b = 180-120
b = 60
Answer:
60°
Step-by-step explanation:
Recall that all triangles have an interior angle sum of 180. In other words:
[tex]\angle A+\angle B +\angle C = 180[/tex]
Plug in the angle values we know:
[tex](80)+(40)+\angle B = 180\\120+\angle B =180\\\angle B = 60\textdegree[/tex]
Find the area of the shaded region
A. 12 ft^2
B. 36 ft^2
C. 40.5 ft^2
D. 18 ft^2
Answer:
The shaded area is 18 ft^2
Step-by-step explanation:
First find the area of the total trapezoid
A = bh
A = 1/2 ( b1+b2) *h
= 1/2 ( 6+12) *6
= 1/2 ( 18)*6
=54
Now find the area of the triangle
A = 1/2 bh
= 1/2 ( 12) * 6
= 36
Subtract the triangle from the trapezoid
54-36
18
The shaded area is 18 ft^2
Answer:
D. 18 sq.ft
Step-by-step explanation:
Lets make it simple and short.
Area of a triangle is 1/2 b h
b = 6
h = 6
Area = 1/2 * 6 * 6
Area = 18 sq.ft
Lines T U and R S intersect lines M N and P Q. Where line T U intersects with lines M N and P Q, right angles are formed. Lines M N and P Q are straight lines that are next to each other and they will never intersect. Lines T U and R S are next to each other and could intersect. Which two statements are both true?
c. Tu | MN and MN || PQ I am done with the interview
a cone with base radius 7 cm has a volume of 308 cm cube find the vertical height of the cone take π 22/7
pls now
Answer:
h=6.003 cm
Step-by-step explanation:
[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]
1/3×22/7×7×7×h=308
h=308/51.3
Answer:
h = 6 cm
Step-by-step explanation:
r = 7 cm
Volume of cone = 308 cm³
[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]
h = 6 cm
Covert the verbal expression into an algebraic expression.
The product of 23 and a number x
Answer:
23×x
=23x
Hope it helps
Answer:
23x
Step-by-step explanation:
"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.
help please, got a little lost in everything
Answer:
375 mm cubed
Step-by-step explanation:
The volume would stay the same because the same number of the same pennies are being used.
If the question was asking for the surface area, then the answer would be different.
Hope that helped!!! k
Answer: 375 mm cubed
Factor completely 2c5 + 44c4 + 242c3. 2c3(c + 11)2 2(c + 11)2 2c3(c + 11)(c − 11) 2c3(c2 + 22c + 121)
Answer:
2c^3(c+11)^2
Step-by-step explanation:
2c^5 + 44c^4 + 242c^3
Factor out the greatest common factor
2c^3(c^2+22c+121)
Recognizing inside the parentheses is (a+b) ^2 where a =c and b = 11
2c^3(c+11)^2
which one represents translation
Answer:
The third one
Step-by-step explanation:
Translation is when it moves
