2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed. Test the hypothesis (at 95% confidence) that there is no difference in the proportion of deaths between the 2 groups. What do you conclude? Calculate the margin of error (E) at 95%.
Answers
Answer:
We conclude that there is difference in the proportion of deaths between the 2 groups.
Step-by-step explanation:
We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.
Let \(p_1\) = proportion of deaths when drivers were not wearing seat belts.
\(p_2\) = proportion of deaths when drivers were wearing seat belts.
So, Null Hypothesis, \(H_0\) : \(p_1=p_2\) {means that there is no difference in the proportion of deaths between the 2 groups}
Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\) {means that there is difference in the proportion of deaths between the 2 groups}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\) ~ N(0,1)
where, \(\hat p_1\) = sample proportion of deaths when drivers were not wearing seat belts = \(\frac{31}{2823}\) = 0.011
\(\hat p_2\) = sample proportion of deaths when drivers were wearing seat belts = \(\frac{16}{7765}\) = 0.002
\(n_1\) = sample of drivers not wearing seat belts = 2823
\(n_2\) = sample of drivers wearing seat belts = 7765
So, the test statistics = \(\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }\)
= 4.438
The value of z test statistics is 4.438.
Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.
Also, Margin of error (E) = \(1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }\)
= \(1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }\)
= 0.00397
Related Questions
A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the chips cost $0.75. After the game, they tallied 175 transactions totaling $262.50.
Represent the linear system in an augmented matrix:
1
1
175
2.5
0.75
262.5
The number of hotdogs sold was
100
.
The number of chips sold was
.
Answers
The augmented matrix representing the system of equations is given as follows:
[1 1 175]
[2.5 0.75 262.5].
The amounts sold were of:
Hot dogs: 75.Chips: 100.How to obtain the amounts?The amounts are obtained via a system of equations, for which the variables are given as follows:
Variable x: number of hot dogs sold.Variable y: number of chips sold.A total of 175 transactions were made, hence:
x + y = 175
y = 175 - x.
They totaled earnings of $262.5, hence:
2.5x + 0.75y = 262.50.
The augmented matrix is:
[1 1 175]
[2.5 0.75 262.5].
Replacing the first equation into the second, the value of x is given as follows:
2.5x + 0.75(175 - x) = 262.5
1.75x = 131.25
x = 131.25/1.75
x = 75.
Then the value of y is given as follows:
y = 175 - 75
y = 100.
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I want a way to solve this question
Answers
Answer:
7 and 7
Step-by-step explanation:
It is asking, what 2 numbers when added together equal 14, but when you multiply them together get the largest number that you can.
7+7 = 14
7*7= 49 which is the largest number you can get.
I hope this helped <3
there are 7 people to be seated in a row. answer the following.A. Find The Number Of Combinations If There Are No Restrictions On The Seating Arrangements. B. There Are Three Friends That Must Sit Together. Find The Number Of Combinations In Which The Three Friends Are Next To Each Other. C. Suppose That An Usher Randomly Assigns The Seats To The 7
Answers
A) The Number of Combinations if there are no restrictions on the seating arrangements are 5040 ways.
B) There are three friends That must sit together
in 36 ways.
C) Three friends are next To each other in 144 different ways.
Total number of people = 7 and seated in a row.
Combination is arrangement of objects in a particular order. The formula of combination is
ⁿCₓ = n!/(n-x)! x!
n --> total number of objects
we have to determine how many ways can 7 be seated in a row.
A) if there are no restrictions on seating arrangement, The number of possible ways = n!
Here, n! = 7!
= 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 ways.
Therefore, there are 5040 ways that the people can be seated when there is no restriction on the seating arrangement.
b) There are three friends that must sit Together. The three persons can be arranged in 3!
The possible number of ways = 3! × 3! × 1
= 3× 2×1 ×3×2×1
= 36
C) If there are three friends must sit next to one another. There are total seven persons . Three persons sit next to one another. The possible number of ways = 3! × 4!
= ( 3 × 2 × 1) × (4 × 3 × 2 × 1)
= 6 × 24
= 144 ways
Therefore, if there are 3 sit next to one another, there are 144 ways of seating arrangement.
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What is 18x4=9xn? Just tell me the answer.
Answers
Answer:
Step-by-step explanation:
x=0
Answer:
8
Step-by-step explanation:
18×4 = 72
And 72 ÷ 9 = 8
So 9×8 would be 72
{1, √2, √√3, 2, √5, ...}
need help knowing the sequence and the 3 next terms
Answers
Answer:
3, 2√2, √7
Step-by-step explanation:
compute the square roots of the next three prime numbers:
√7
√11
√13
Therefore, the next three terms of the sequence are:
{1, √2, √3, 2, √5, √7, √11, √13}
chatgpt
chat
Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
Question Content Area
a. What was the book value of the equipment at December 31 the end of the fifth year?
Answers
The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.
Define straight line methodThe straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:
Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life
The annual depreciation expense for the equipment is:
Depreciation expense = (cost - residual value) / useful life
Depreciation expense = ($212,000 - $14,000) / 15
Depreciation expense = $12,533.33 per year
The total depreciation expense for the first five years is:
Total depreciation expense = Depreciation expense x number of years
Total depreciation expense = $12,533.33 x 5
Total depreciation expense = $62,666.65
To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:
Book value = Cost - Total depreciation expense
Book value = $212,000 - $62,666.65
Book value = $149,333.35
Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.
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(Conditionals)
TRUE OR FALSE:
If a number is a perfect square, then it has only 3 factors.
Answers
Answer:
False
I hope this helps!
If four is subtracted from twice a number, the result is fourteen what is the equation
Answers
Answer:
2x - 4 = x - 10
Step-by-step explanation:
The sides of a triangle have lengths of 2x – 1, x + 3, and 3x – 4. Which
of the following describes the perimeter of the triangle in terms of x?
F. 5X-8
B6x3 – 12
G. 6x + 9
J. 6x-2
Answers
i am pretty sure it is g .
a person pays a loan of Rs. 3900 in monthly installments each in installment being less than the former by Rs. 20 ,the amount of first is Rs.400 in how many installment will entire amount be paid ? give reason
Answers
Answer:
15 installments
Step-by-step explanation:
3900 = Σ \(\left \ {{x=n} \atop {x=1}} \right.\) 400 - 20*(n - 1)
Which of these is NOT a way to show that two figures are congruent?
Answers
If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.
What is Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is the condition to be congruent?If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
here, we have,
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In Δ PQR and ΔXYZ, as shown in figure,
we can identify that PQ = XY, PR = XZ,
and QR = YZ
and ∠P = ∠X,
∠Q = ∠Y and ∠R = ∠Z.
Then we can say that Δ PQR ≅ ΔXYZ.
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each function
f(x)=-4x-5;
ion for
Find ƒ(1)
for the given
Answers
When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.
The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.
Replacing x with 1, we have:
ƒ(1) = -4(1) - 5
Simplifying further:
ƒ(1) = -4 - 5
ƒ(1) = -9
Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.
Let's break down the steps taken to arrive at the solution:
1. Start with the function f(x) = -4x - 5.
2. Replace x with 1 in the function.
3. Evaluate the expression by performing the necessary operations.
4. Simplify the expression to obtain the final result.
In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.
It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.
Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.
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a carpenter has 6 boards that are each 7/8 yard long. how many 3/4 yard sections of board can he construct
Answers
The number of sections of board that he can construct will be equal to 7.
We are given that:
A carpenter has 6 boards.
Length of each board = 7 / 8 yard long
Now, we will use multiplication.
Total length of cardboards available = 7 / 8 × 6 yards
Total length = 42 / 8 yards
Total length = 21 / 4 yards.
Now, 3/4 yard sections of board that he can construct will be:
Number of sections of board = 21 / 4 ÷ 3 / 4
Number of sections of board = 21 / 3
Number of sections of board = 7
Therefore, the number of sections of board that he can construct will be equal to 7.
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Find the mean of the
data set:
14, 19, 13, 22,7
Answers
Answer:
Add up all the numbers and divide it by how many numbers there are.
14+19+13+22+7=75
75÷5 =15
Find what minimum population size you need to have if you have a 99% confidence, 100 standard deviation and want a size 3 margin of error
Answers
A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.
How to calculate the minimum population size?To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:
n = [(z-value × SD) / ME]²
Where:
n = the minimum sample size required
z-value = the critical value for the desired confidence level (99% in this case)
SD = the known standard deviation (100 in this case)
ME = the desired margin of error (3 in this case)
First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.
Substituting the values into the formula, we get:
n = [(2.576 × 100) / 3]²
Simplifying this expression, we get:
n = 7373.08
Therefore, we would need a minimum population size of approximately 7373.
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Plz someone help me.
Answers
Answer:
825 students
Step-by-step explanation:
multiply the ratio by the amount of students
1000*0.825=825
The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answers
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
2. Suppose the price of good x increased from 4 birr to 5 birr. Because of change price of good x, quantity demand of good y changed from 5,000 to 6,250. a. Find cross price elasticity of demand b. What types of goods (good x and good y) are?
Answers
Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.
Let's calculate the cross-price elasticity of demand using the given information:
a. Find the percentage change in quantity demanded of good Y:
Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100
Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%
b. Find the percentage change in the price of good X:
Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100
Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%
Now, we can calculate the cross-price elasticity of demand:
Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X
Cross-Price Elasticity of Demand = 25% / 25% = 1
b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:
If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.
Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.
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Answer:
Step-by-step explanation:
Which algebraic function has a smaller rate of change than the equation?
f(x)=2x−9
Answers
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble?
25%
62.5%
20%
41.7%
Answers
Answer:
20%
Step-by-step explanation:
The theoretical probability of drawing a red marble can be found by dividing the number of red marbles by the total number of marbles in the bag:
P(red) = number of red marbles / total number of marbles
P(red) = 5 / (5 + 8 + 12)
P(red) = 5 / 25
P(red) = 0.2
So the theoretical probability of randomly drawing a red marble is 20%, which corresponds to option (C).
00:00
The city council in Middlefield wants to know if residents are in favor of a traffic camera at the main intersection in town. Drag tiles to match each
term to the example it best describes. Each tile may be used only once.
Representative Sample
Population
NOT a Representative Sample
Term
Example
Drivers who reside in Middlefield
Residents of Middlefield
Residents randomly chosen from the town register
Answers
Answer:
Matching Tiles with Terms:
Term Example
NOT a Representative Sample Drivers who reside in Middlefield
Population Residents of Middlefield
Representative Sample Residents randomly chosen from the
town register
Step-by-step explanation:
Population includes all the residents of Middlefield.
Representative Sample is a population subset that accurately reflects the characteristics of the population. For example, the subset of residents who are randomly chosen from the town register is an unbiased and representative sample.
NOT a Representative Sample: For example, drivers who reside in Middlefield do not represent the characteristics of the population of Middlefield.
he mean life of a tire is 30,000 km. The standard deviation is 2000 km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
Answers
The conclusion is that 68% of all tires will have a life between 28000 km and 32000 km.
How to use the Empirical Rule of statistics?
The empirical rule in statistics states that for a normal distribution,
68% of the distribution are within one standard deviation from the mean.95% are within two standard deviation from the mean.99.7% are within three standard deviations from the mean.We are given;
Mean (μ) = 30000 km
Standard deviation (σ) = 2000 km
Using the empirical rule of 68% which lies within one standard deviation from the mean, we have;
μ ± σ = 30000 ± 2000 = (28000, 32000)
Thus, we conclude that 68% of all tires will have a life between 28000 km and 32000 km.
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help with this question
Answers
9514 1404 393
Answer:
A = 49π/36 or 59π/36
Step-by-step explanation:
The given angle is coterminal with the same angle modulo 2π.
(563/36)π = 14π +(59/36)π
so the coterminal angle is 59π/36 ≈ 1.6389π, a 4th-quadrant angle. The 3rd-quadrant angle with the same sine value is found by subtracting this angle from 3π:
A = 3π -(59π/36) = 49π/36
The two values of A that satisfy the equation are ...
A = 59π/36A = 49π/36_____
In degrees, the two angles are 245° and 295°.
3,998-(-7)= can you please help me with this problem
Answers
Answer:
4005
Step-by-step explanation:
3,998 - (-7) = ?
Two negative signs will make a positive sign.
3,998 - (-7) = 3998 + 7 = 4005
So, the answer is 4005
What is 3.59 rounded to the nearest whole number?
Answers
Answer:
its 4 ezy
Step-by-step explanation:
please mark as brainlists
look at the picture and pls hurry i’m failing algebra and this will help a lot
Answers
UmumumumumumumumumumumumuAnswer:
Step-by-step explanation:
n-6m-8 for n help! please
Answers
Answer:
n=6m+8
Step-by-step explanation:
we hav to get n by itself
so start easy and add 8 to theother side
n-6m=8 then take 6m and add it the other side
n=6m+8 and there you go
Answer:
Step-by-step explanation:
n - 6m = 8
n = 8 + 6m
How many triangles can be constructed with three sides measuring 11 meters, 16 meters, and 26 meters?
оо
0 1
O more than one
Answers
Answer:
only one.
We can construct onle one triangle with unique measurements.
Answer:
1 triangle can be constructed
Step-by-step explanation:
11. The area of a circle is πr2 where r is the length of the radius. Thus, one could take the measure of the central angle in degrees and ____________ _________. Then, multiply that result by πr2.
Answers
The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²
What is the area of the sector?We will use the following points to find the area of the sector;
First of all, the angle that is formed in a full rotation is 2π.
The area of a circle is given by the formula; A = πr²
The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π
Thus, the area of a sector is given by the formula;
A = (θ/2π) * πr²
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1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Answers
Answer:
(3)1. Find the coordinates of all points where the lines
x + y = 8, y = 5, and x = 1 intersect.
Step-by-step explanation:
this answer
The coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are (0, 5), (1, 0), (3, 5) and (1, 7).
Given that;
The equation of lines is,
x + y = 8
y = 5
x = 1
Now all the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect are find as,
x + y = 8
Put y = 5;
x + 5 = 8
x = 8 - 5
x = 3
Put x = 1;
1 + y = 8
y = 8 - 1
y = 7
Therefore, the points are (0, 5), (1, 0), (3, 5) and (1, 7).
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