A battery producer claimed that the mean lifetime of a battery produced by his factory was 30 hours. A competitor thought that the figure was too high and took 8 batteries at random and the lifetime of each is as follows:
a) Can the claim by the battery producer be accepted at the 5% significant level? b) Can the claim by the battery producer be accepted at the 20% significant level?
Answers
The claim of the producer can be accepted at 5% significant level since the 30 hours is within 21.8118 < X < 30.932
The claim of the producer cannot be accepted at 20% significant level since the 30 hours is not within 23.648 < X < 29.102
How to check the claim of the producerThe claim is done using t score as the sample is less than 30. the formula for t scores is as follows
= x-bar ± t(s/√n)
from the given data the mean is calculated
sample mean, x-bar = (15 + 28 + 33 + 24 + 28 + 25 + 31 + 27) / 8
= 211/8
= 26.375
sample standard deviation, s
variance = (15 - 26.375)² + (28 - 26.375)² + (33 - 26.375)² + (24 - 26.375)² + (28 - 26.375)² + (25 - 26.375)² + (31 - 26.375)² + (27 - 26.375)²) / (8 - 1)
= 207.875 / 7
= 29.696
standard deviation = √variance
= √29.6964
= 5.45
Definition of variables
mean, x-bar = 26.375
standard deviation, s = 5.45
sample size, n = 8
significance level = 5%
confidence level = 1 - significance level = 1 - 0.05 = 0.95 = 95%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 8 - 1 =7
t score for 95% confidence level and df of 7 = 2.365
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 2.365 (5.45 / √8)
= 26.375 ± 4.557
= 21.8118 < X < 30.932
t score for 20% significant level and df of 7 = 1.415
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 1.415 (5.45 / √8)
= 26.375 ± 2.727
= 23.648 < X < 29.102
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Related Questions
t^2-t-6/t^2+6+9 • t+3/t^2-4
Answers
A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the model:
Salary = β0 +β1 Service + ε. The following ANOVA table below shows a portion of the regression results.
df SS MS F
Regression 1 555,420 555,420 7.64
Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Which of the following is the monthly salary of an employee that has worked for 48 months at the bank?
rev: 11_17_2017_QC_CS-109762
$441.
$785.
$1,050.
$1,226.
Answers
The monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.
The given table is:
Df SS MS F
Regression 1 555,420 555,420 7.64
Residual 27 1,962,873 72,699
Total 28 2,518,293
Coefficients Standard Error t-stat p-value
Intercept 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
We have to find the monthly salary of an employee that has worked for 48 months at the bank.
Salary = β(0)+ β(1) Service
y = β(0)+ β(1)x
where, Service = x(in months)
Service = y(in $)
From the table
y = 784.92+9.19x
If x=48 months
Then, y = 784.92+9.19(48)
y = 784.92+441.12
y = 1226.04
Hence, the monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.
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16. The points graphed below show the how completing homework can affect a student's test scores.
What is the meaning of the slope of the line in
the context of the problem?
A student's test score goes down 20 points
every time they complete 2 homework
assignments
A student's test score goes up 9 points every
time they complete 1 homework assignment
A student's test score goes down 10 points
every time they complete 1 homework
assignment
A student's test score goes 80 points every
time they complete 1 homework assignment
Answers
The meaning of slope of the line in the context of the problem is a student's test score goes up 9 points every time they complete 1 homework assignment.
What is Slope?Slope of line is shows how much a line is inclined with respect to the X axis. In other words, it can also be defined as the change in y coordinates with respect to the change in x coordinates.
Slope of the line can be calculated if two points (x₁, y₁) and (x₂, y₂) are given as,
Slope = (y₂ - y₁) / (x₂ - x₁)
From the graph, take any two points on the line.
For instance, we take initial point (1, 20) and final point (10, 100).
Slope = (100 - 20) / (10 - 1)
= 80/9
≈ 9
From the definition of slope, slope equals 9 means y values goes 9 points up with respect to one unit up in the x values.
Hence we got that a student's test score goes up 9 points every time they complete 1 homework assignment.
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Consider the drawing and information below. The drawing is NOT to scale.
1.What is m < 2 show work and calculations.
2. What is m < 4 show your work and calculations.
Answers
Answer:
m∠2 = 110°
m∠4 = 110°
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Transitive Property of Equality
If any angles are congruent to the same angle, then they are congruent to each other.
--------------------------------------------------------------------------------------
As line p is parallel to line q, according to the Corresponding Angles Postulate:
⇒ m∠2 = m∠10
According to the Vertical Angles Theorem:
⇒ m∠10 = m∠13
According to the Transitive Property of Equality:
⇒ m∠2 = m∠13
Therefore:
⇒ 8x + 14 = 10x - 10
⇒ 8x + 14 - 8x = 10x - 10 - 8x
⇒ 14 = 2x - 10
⇒ 14 + 10 = 2x - 10 + 10
⇒ 24 = 2x
⇒ 2x = 24
⇒ 2x ÷ 2 = 24 ÷ 2
⇒ x = 12
Substitute the found value of x into the expression for the measure of angle 2:
⇒ m∠2 = 8(12) + 14
⇒ m∠2 = 96 + 14
⇒ m∠2 = 110°
--------------------------------------------------------------------------------------
As line p is parallel to line q, according to the Corresponding Angles Postulate:
⇒ m∠12 = m∠4
⇒ 15y + 5 = 13y + 19
⇒ 15y + 5 - 13y = 13y + 19 - 13y
⇒ 2y + 5 = 19
⇒ 2y + 5 - 5 = 19 - 5
⇒ 2y = 14
⇒ 2y ÷ 2 = 14 ÷ 2
⇒ y = 7
Substitute the found value of y into the expression for the measure of angle 4:
⇒ m∠4 = 13(7) + 19
⇒ m∠4 = 91 + 19
⇒ m∠4 = 110°
Which functions have a vertex with a x-value of 0? Select three options.
Of(x) = |x|
f(x) = x + 3
f(x) = 1x + 31
f(x) = 1x1-6
Of(x) = x + 31-6
Answers
The functions that have a vertex at x = 0 are (a) f(x) = |x| and (d) f(x) = |x| - 6
How to determine the function from the vertexFrom the question, we have the following parameters that can be used in our computation:
The absolute functions in the options
As a general rule;
A absolute functions can be represented as
f(x) = a|x - h| + k
Where
Vertex = (h, k)
A vertex that has x value of 0 means
(h, k) = (0, k)
So, we have
f(x) = a|x - 0| + k
Evaluate
f(x) = a|x| + k
Looking at the options, we have
f(x) = |x| and f(x) = |x| - 6
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Select the table that represents a liner function. (Use graph if necessary)
Answers
The table that represents a linear equation is the first one, and the line is:
y = 5x + 5
Which table represents a linear function?
To check which table represents a linear function, you need to identify the increases in x, and check that al the increases/decreases in y are constant.
For example, if you look at the last table:
x = 0, 1, 2, 3
y = 1, 2, 4, 8
First x goes from 0 to 1, so 1 unit increase.
y goes from 1 to 2, 1 unit increase.
Then x goes from 1 to 2, 1 unit increase.
y goes from 2 to 4, 2 units increase.
The increase is not constant, thus it is not a linear equation.
The tables 2 and 3 can be discarded because have both increases/decreases.
Table 1 is the one that represents a linear equation:
x: 0, 1, 2, 3
y: 5, 10, 15, 20
Where the increases in y are always of 5 units, and the linear equation is:
y = 5*x + 5
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Evaluate the function when x = 3, x = 0, and x = -4. (Lesson 4.8)
14. f(x) = -4x + 3
12. h(x) = − 8x
13. g(x) = 5x - 9
16. h(x) = 1.4x
15. g(x)=-3x - 12
17. f(x) = 1/4x
12-17 please
Answers
The cost of a plumber consists of two parts: the fixed costs and the hourly rate.
One piece of work takes the plumber 5 hours and costs £155.
Another piece of work takes the plumber 8 hours and costs £230.
(a) i) What is the fixed cost of the plumber?
ii) What is the hourly rate for the plumber?
Answers
The fixed cost of the plumber is £30 and the hourly rate for the plumber is £25.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Let the fixed cost of a plumber is y.
Let the number of hours of work done be x.
As per the first condition, that one piece of work takes the plumber 5 hours and costs £155.
Then, the equation according to the statement will be,
y + 5x = £155 (i)
In the second condition, another piece of work takes the plumber 8 hours and costs £230.
Then, the equation according to the statement will be,
y + 8x = £230 (ii)
Now, subtract equation (ii) from the equation for the value of x,
y + 5x = £155
y + 8x = £230
-3x = -75
x = £25
Put x = £25 in equation (i)
y + 5x = £155
y + 5(25) = 155
y = 155 - 125
y = £30.
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Information for Questions 5-7: The Annual Survey of Colleges in the U.S. also reports on the average amount of student loan debt by state. The most recent data by state showed an approximately normal shape with a minimum average amount of
$19,000
and a maximum average amount of
$38,000
. Use the minimum and maximum value and the normal shape to estimate the mean and standard deviation of the data for the 50 states. (Mean and standard deviation have been rounded to the nearest
$100
.) a. mean
=$25,000;
standard deviation
=$3,500
b. mean
=$26,800;
standard deviation
=$2,100
c. mean
=$26,800;
standard deviation
=$3,700
d. mean
=$28.500;
standard deviation
=$1,800
e. mean
=$28,500;
standard deviation
=$3,200
A federal study of student loan debt plans to focus on those states with the highest amounts of student loan debt. The study plans on targeting those states that fall in the top
2.5%
in terms of average student loan amounts. What is the cutoff point that would place a state in the top
2.5%
based on student loan debt? (Use the mean and standard deviation estimates from Question #5.) a.
$38,100
b.
$34,900
c.
$31,700
d.
$32,500
e.
$22,100
Answers
The correct answer is $34900.
X : Average amount of loan of student debt by state .
X = N ( μ = $28500 , σ² = ( 3200 )² )
To find : What is the cutoff point that would place a state in top 2.5%
Let it be X
P( X > x ) = 0.025
P(X-μ/σ > X - 28500/3200) = 0.025
P(z >Z ) = 0.025
1 - P(z<Z ) = 0.025
P(z<Z ) = 0.975
φ(z) = 0.975
Z = φ⁻¹(0.975)
X - 28500/3200 = 1.96
X = 34772
i.e; P(X > 34772) = 0.025
Since, it is nearly equal to $34900 option b is correct.
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HELPP!!!!! HURRY!!!! Function g(x) = |x − 9| is a transformation of function f(x) = |x|. What effect does the value 9 have on the graph of function f? A. It translates the graph 9 units to the left. B. It translates the graph 9 units to the right. C. It vertically compresses the graph by a factor of 9. D. It vertically stretches the graph by a factor of 9.
Answers
Answer:
C
Step-by-step explanation:
Answer:
B: It translates the graph 9 units to the right.
Step-by-step explanation:
The value 9 has the effect of translating the graph of function f(x) = |x| 9 units to the right. This is because the transformation g(x) = |x - 9| is obtained from f(x) = |x| by subtracting 9 from the argument of the absolute value function. This has the effect of shifting the graph of f(x) to the right by 9 units.
Therefore, the correct answer is B: It translates the graph 9 units to the right.
To find the slope of a curve at a given point, we simply differentiate the equation of the curve and find the first derivative of the curve, i.e., dy/dx.
Answers
To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result
The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line
To find the slope of the curve at a given point
First differentiate the given equation of the curve with respect to x
That is dy / dx.
The derivative of the equation of the curve is the slope of the curve.
In next step substitute the value of x in the slope of the curve
The result will be the slope of the curve at a given point
Therefore, these are the steps to find the slope of the curve
I have answered the question in general, as the given question is incomplete
The complete question is:
How to find the slope of a curve at a given point?
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In the United States about 7% of the male population and about 0.4% of the female population is red-green color blind ( that is they cannot distinguish red from green, or see red and green differently from how others do). The population in the United States consist of about 49% males and 51% females. A person is randomly selected.
Let M be the event that the person is male, let F be the event that the person is female, let CB be the event that the person is red-green color blind, and let NC be the event that the person is not red-green color blind
A. Find P(CB \mid M)
B. Find P(CB \cap M)
C. Find P(CB)
Find P(M \mid CB)
Answers
Ans (A) P(CB/M) is 0.07
Ans (B) P(CB ∩ M) is 0.0343
Ans (C) P(CB) is 0.03634
Ans (D) P(M/CB) is 0.94386
Let the population be 100.
Therefore,
No. of males (M) = 49
No. of females (F) = 51
No. of colourblind males =
[tex]\frac{7}{100} * 49 = \frac{343}{100} = 3.43[/tex]
No. of colourblind females =
[tex]\frac{0.4}{51} * 100 = 0.204[/tex]
Total colourblind people (CB) = 3.43 + 0.204 = 3.634
Ans (A)
P(CB/M) = P(CB ∩ M)/P(M) = 3.43/49 = 0.07
Ans (B)
P (CB ∩ M) = 3.43/100 = 0.0343
Ans (C)
P(CB) = 3.634/100 = 0.03634
Ans (D)
P (M/CB) = P(M ∩ CB)/P(CB) = 3.43/3.634 = 0.94386
These are the answers.
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Hurry please
Which line has a y-intercept of 2 and an x-intercept of -3?
W.
X.
Y.
Z.
Answers
Answer:
The answer is going to be y because you can see that it hits 2 on the y-intercept and -3 on the x-intercept
Step-by-step explanation:
Here is the one that you need
Please help will mark Brainly
Answers
Answer:
Below
Step-by-step explanation:
The first set of graphs is the correct one....it shows Y = constant 18
and shows Z as starting at 10 (deposit) THEN INCREASING 2 per hour....
where they cross is 4 hours and charges are the same
Your family ate a delicious meal at Jimmies of Savin Rock. The meal itself cost $147.25, you want to leave 20% tip and there was 7.35% tax added
Answers
Answer:
27.29 honestly this is a wild guess
Step-by-step explanation:
7.35% of 147.25 = 10.82
147.25-10.82=136.43
20% of 136.43 = 27.286(27.29)
I’m confused on this question
Answers
Answer: 3 of the squares should go down then 8 to the right.
Step-by-step explanation:
it just wants you to say how it was translated so take the corresponding points like p and p’ then count of many tiles it move to the right and then down to get from p to p’ you’ll see that it’s 8 right and 3 down.
hope this helps!
The coordinates of C are ( 4 , 4 ) , and the midpoint of CD ¯ is at M ( - 2 , - 6 ) . What are the coordinates of point D
Answers
Answer:
D (-8, -16)
Step-by-step explanation:
(4+x)/2 = -2
4+ x = -2 · 2
4 + x = -4
x = -4 - 4
x = -8
(4 + y)/2 = -6
4 + y = -6 · 2
4 + y = -12
y = -12 - 4
y = -16
Parallel and Perpendicular lines Block
Answers
By observing the figure we can make the pairs as
∠1 ≅ ∠3 ---------(Opposite angles)
∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)
∠4 ≅ ∠6 ---------(Alternate angles)
∠3 ≅ ∠5 ---------(Alternate angles)
What are opposite angles and Alternate angles?
Opposite angles are angles that are located opposite each other, with respect to a straight line or a transversal. They are also called vertically opposite angles.
Alternate angles are angles that are located on opposite sides of the transversal and on the same side of the straight line or the transversal. They are also called corresponding angles.
In the given figure,
By observing the opposite angles and alternate angles we can fill the blocks,
∠1 ≅ ∠3 ---------(Opposite angles)
∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)
∠4 ≅ ∠6 ---------(Alternate angles)
∠3 ≅ ∠5 ---------(Alternate angles)
Hence, we have found the opposite angles and alternate angles from the figure.
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A recipe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 2 gallons of milk?
Answers
Answer:
what we cookin ma boi
Step-by-step explanation:
How could you organize the weighting and grades information differently so that Oscar's and Reagan's final grades are given by WG?
Answers
Answer i just need points
Step-by-step explanation: maybe 90
Given the drawing as shown below and that p parallel q, which of the following cannot be supported?
Answers
Answer: It's B
Step-by-step explanation:
It shows that Angle B is congruent to angle g but it actually isnt
Answer:
B. ∠b ≅ ∠g
Step-by-step explanation:
Supplementary angles
Two angles whose measures sum to 180°.
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Same-side Interior Angles Theorem
When two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
------------------------------------------------------------------------------------------
Statement A
∠f and ∠h are vertical angles. Therefore, according to the Vertical Angle Theorem, ∠f ≅ ∠h.
Statement C
As ∠d and ∠h are the interior angles on the same side of the transversal [tex]\ell[/tex], according to the Same-side Interior Angles Theorem, ∠d and ∠h are supplementary.
Statement D
∠a and ∠b are a linear pair, therefore ∠a and ∠b are supplementary.
Therefore, Statement B cannot be supported by the evidence shown.
Need answers for all parts.
Answers
(a) The balance be at the end of the year is $502.53.
(b) The Effective annual interest rate is 0.5%.
(c) The Effective annual interest rate must be less than 6%.
What is effective annual interest rate?
The percentage of interest on a loan or financial product that would apply if compound interest built up over a year without any payments would be called the effective interest rate, also known as the effective annual interest rate, annual equivalent rate, or simply effective rate.
Given:
P = $500, n = 12, r = 0.5% = 0.005, t = 1
So, the balance be at the end of year is,
[tex]A = P(1+\frac{r}{n})^n^t \\A = 500(1+\frac{0.005}{12})^1^2^*^1 \\A = 500(1.00042)^1^2\\A = 502.53[/tex]
Now to find the effective annual interest rate,
Effective annual interest rate = [tex]= (1+\frac{r}{n})^n-1 = (1+\frac{0.005}{12})^1^2 - 1= 0.005[/tex]
Effective annual interest rate = 0.5%
So, the Effective annual interest rate must be less than 6%.
Hence,
(a) The balance be at the end of the year is $502.53.
(b) The Effective annual interest rate is 0.5%.
(c) The Effective annual interest rate must be less than 6%.
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check the screenshot
Answers
Answer:
a = 1
h = 4
k = -4
Step-by-step explanation:
Find the inverse of the equation
Y=5/x-1
Answers
The inverse of the equation is y = (5/x) + 1
How to determine the inverse of the equation?From the question, we have the following parameters that can be used in our computation:
y = 5/(x - 1)
Start by swaping the positions of x an dy
So, we have the following representation
x = 5/(y - 1)
So, we have
x(y - 1) = 5
Divide both sides by x
y - 1 = 5/x
Add 1 to both sides
y = (5/x) + 1
Hence, the inverse is y = (5/x) + 1
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Let Y1 and Y2 be independent random variables, both uniformly distributed on (0, 1). Find the probability density function for U = Y1Y2.
Answers
The probability density function as calculated from the given data is fₙ (u)=−ln(u).
Y1 and Y2 are independent random variables and both have uniform distribution over the interval (0,1)(0,1).
We need to find out the density function of U = Y1Y2 using the method of transformations.
Density function of Y1
= 0 or 1
Density function of Y2
= 0 or 1
Therefore joint density function is,
( 0 , 1) where, 0≤y 1 ≤1,0≤y 2 ≤1
There are 3 steps to find joint density function of Y and U using methods of transformations
Hence, the required probability density function is :
fₙ (u)=−ln(u)
An independent random variable is one that has no effect on the other random variables in your experiment. In other words, it has no bearing on the likelihood of another occurrence occurring.
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URGENT! Please help with the image attached!
Answers
The missing angle in the parallel lines is as follows;
m∠STW = 125 degreesHow to find the angles when parallel line are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.
Therefore, let find angle m∠STW .
VX and SU are parallel lines. RY is the transversal line.
Hence,
m∠VWY = 125 degrees
m∠VWY = m∠STW (corresponding angles)
Corresponding angles are congruent to each other.
Therefore.
m∠STW = 125 degrees
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Choose the number that is greater than:
4.526 x 10^6
OA) 5.79 x 105
OB) 9.99 x 105
OC) 4.123 x 106
OD) 55,264,900
Answers
Answer: C) 4.123 x 106
Step-by-step explanation:
Use pentagon ABCDE to answer the following. What are the coordinates of B after the pentagon is rotated 90 degrees about the origin?
Answers
The coordinates of B after the rotation of 90 degrees about the origin is (c) (-5, 1)
How to determine the coordinates of B after the rotationThe figure of the pentagon missing in the question is added at the end of this solution as an attachment
From the question, we have the following parameters that can be used in our computation:
Coordinate of point B = (1, 5)
Also, from the question, we have the transformation to be
Rotation of 90 degrees about the origin
Mathematically, the rotation of 90 degrees about the origin can be represented as
(x, y) → (-y, x)
Substitute the known values in the above equation, so, we have the following representation
Coordinate of point B after rotation = (-5, 1)
Hence, the coordinate of point B after the rotation is (c) (-5, 1)
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8 ft 10 ft Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate . A = [?]ft? Notice that only half of the circle is included in the figure!
Answers
find the area of the rectangle;
w x l = 8 x 10 = 80ft^2
circle;
pi(r)^2
r = 4
pi(4)^2
pi(16) = 50.24
80 + 50.24 = 130.24
A set of data items is normally distributed with a mean of 300 and a standard deviation of 60. Why’d the data item in this distribution that corresponds to the given z-score
Z= 2.5
Answers
The data item that corresponds to the z-score of 2.5 is 450.
What is Standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.
A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation. The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, makes it a valuable statistic.
As, x = z×s + u, where z=2.5, s=60, u=300
⇒ x = 2.5×60 + 300
⇒ x = 150 + 300
⇒ x = 450
The data item that corresponds to the given z-score is 450.
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