Could anyone elaborate on how they determined whether this is a one-tailed, two-tailed, or upper-tailed test? Could you also explain how to determine which section of the graph on a bell curve that gets shaded in?
A company’s call center advertises that they resolve 80% of its customer calls by using automated voice options. A customer who has called in many times and rarely had issues resolved through the automated options believes that 80% is an overstatement. A significance test was done, and a test statistic was calculated. Assume the conditions for inference were met.
H0: p = 0.80
Ha: p < 0.80
p = The true proportion of all customer calls that are resolved by using automated options
Calculate the P-value, given that the resulting test statistic was z = –1.389.
Answers
Answer:
1. State the claim H0 and the alternative, Ha
2. Choose a significance level or use the given one.
3. Draw the sampling distribution based on the assumption that H0 is true, and shade the area
of interest.
4. Check conditions. Calculate the test statistic.
5. Find the p-value.
6. If the p-value is less than the significance level, α, reject the null hypothesis. (There is enough
evidence to reject the claim.)
If the p-value is greater than the significance level, α, do not reject the null hypothesis.
(There is not enough evidence to reject the claim.)
(You can use the p-value to make a statement about the strength of the evidence against H0
without using α, e.g., p>.10 implies “little or no evidence against H0”, .05< p ≤ 10 implies
“some evidence against H0”, .01 < p ≤ .05 implies “good evidence against H0”, .001 < p ≤ .01
implies “strong evidence against H0”, p ≤ .001 implies “very strong evidence against H0”.)
7. Write a statement to interpret the decision in the context of the original claim.
Test statistics: (Step 3)
Hypothesis testing for a mean (σ is known, and the variable is normally distributed in the
population or n > 30 ) z
x
n
=
− µ
σ
0
(TI-83: STAT TESTS 1:Z-Test)
Hypothesis testing for a mean (σ is unknown, and the variable is normally distributed in the
population or n > 30 ) t
x
s
n
=
− µ0
(TI-83: STAT TESTS 2:T-Test)
Hypothesis testing for a proportion (when np and n p 0 0 ≥ 10 1 10 ( ) − ≥
(TI-83: STAT TESTS 5:1-PropZTest)
Step-by-step explanation:
i think that it?
Answer:
0.0823
Step-by-step explanation:
Related Questions
Choose the correct phrase for 8n
A 8 plus n
B 8 divided by n
C 8 times n
Answers
Each person at a party shook hand with everyone else exactly once. There were 66. Handshakes. How many people were at the party ?
Answers
Let there be 'n' persons at the party.
Since each person shakes hand with every other person exactly once, the total number of handshakes will be the number of ways of selecting two person from the party.
Consider that the number of ways of selecting 'r' objects from 'n' distinct objects is given by,
\(^nC_r=\frac{n!}{r!\cdot(n-r)!}\)So the number of ways of selecting 2 from 'n' people at the party will be,
\(\begin{gathered} ^nC_2=\frac{n!}{2!\cdot(n-2)!} \\ ^nC_2=\frac{n\cdot(n-1)\cdot(n-2)!}{2\cdot1\cdot(n-2)!} \\ ^nC_2=\frac{n\cdot(n-1)}{2} \end{gathered}\)Given that the total number of handshakes is 66,
\(\begin{gathered} \frac{n\cdot(n-1)}{2}=66 \\ n^2-n=132 \\ n^2-n-132=0 \end{gathered}\)Solve the above quadratic equation using the quadratic formula,
\(undefined\)someone pleaseee helppppp
Answers
Consider the following series. [infinity] Σn = 1 4^(n + 1) 5^−n. Determine whether the geometric series is convergent or divergent. Justify your answer. O Converges; the series is a constant multiple of a geometric series. O Converges; the limit of the terms, an, is 0 as n goes to infinity. O Diverges; the limit of the terms, an, is not o as n goes to infinity. O Diverges; the series is a constant multiple of the harmonic series.
Answers
Converges; the series is a constant multiple of a geometric series. Option A
The given series can be written as:
\(\sum n=1 to \infty 4^{(n+1)} * 5^{(-n)\)
= \(4 * \sum n=1 to \infty (4/5)^n\)
This is a geometric series with first term a=4 and common ratio r=4/5. The series converges if and only if |r| < 1. Here, |r| = 4/5 < 1, so the series converges.
The sum of a convergent geometric series with first term a and common ratio r is given by:
sum = a / (1 - r)
Applying this formula, we get:
sum = 4 / (1 - 4/5) = 4 * 5 = 20
Therefore, the given series converges to 20.
The correct answer is option (a) Converges; the series is a constant multiple of a geometric series.
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The horse racing record for a 1.50-mi track is shared by two horses: Fiddle Isle, who ran the race in 147 s on March 21, 1970, and John Henry, who ran the same distance in an equal time on March 16, 1980.What were the horses' average speeds in a) mi/s? b) mi/h?
Answers
The horses' average speeds are approximately:
(a) mi/s: 0.0102 mi/s
(b) mi/h: 58.06 mi/h
To calculate the horses' average speeds, we need to calculate the speed as distance divided by time.
We have:
Distance: 1.50 miles
Time: 147 seconds
(a) To calculate the average speed in mi/s, we divide the distance by the time:
Average speed = Distance / Time
Speed of Fiddle Isle = 1.50 miles / 147 seconds ≈ 0.0102 mi/s
Speed of John Henry = 1.50 miles / 147 seconds ≈ 0.0102 mi/s
(b) To calculate the average speed in mi/h, we need to convert the time from seconds to hours:
Average speed = Distance / Time
Since 1 hour has 3600 seconds, we can convert the time to hours:
Time in hours = 147 seconds / 3600 seconds/hour
Speed of Fiddle Isle = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h
Speed of John Henry = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h
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given a multi-value attribute with a variable number of values, for which we need to process independently the values, it is recommended to consider a new dependent entiy to represent the values
Answers
Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.
Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.
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Kaitlin is riding in a bike race that goes through a valley and
Answers
Given:
The altitude for checkpoint 2 is -47.
The altitude for checkpoint 3 is -216.
The altitude for checkpoint 4 is 2,001.
Required:
a) we need to find the altitude of checkpoint 4 higher than checkpoint 2.
b) we need to find the altitude of the top of the hill when that rises 329 feet about the checkpoint 3.
Explanation:
a)
The difference between 2001 and -47 is
\(2001-(-47)=2001+47=2048.\)Checkpoint 4 is 2048 ft higher than checkpoint 2.
b)
Add 329 to the altitude of the checkpoint 3.
\(-216+329=113\)The altitude of the top of the hill is 113 ft.
Final answer:
a) Checkpoint 4 is 2048 ft higher than checkpoint 2.
b) The altitude of the top of the hill is 113 ft.
Express the following phrase as an algebraic expression.
5 less than y
Answers
6(c+3) – 4(c + 4)
please help what is the answerrrrrrrr????
Answers
Answer:
Step-by-step explanation:
6c + 18-4c + 16
Solving like terms
2c + 34
Answer: 2c + 2
6(c + 3) - 4(c + 4)
= 6c + 18 - (4c + 16)
= 6c + 18 - 4c - 16
= 2c + 2
Step-by-step explanation:
Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Answers
The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives
How to find the minimum number of sets of knives Kaj should buy?Number of knives needed by the restaurant = at least 736 knivesNumber of knives currently available at the restaurant = 155 knivesEach set of knives = 12Number of sets of knives needed to buy = x155 + 12x ≥ 736
substract 155 from both sides12x ≥ 736 - 155
12x ≥ 581
divide both sides by 12x ≥ 581 / 12
x ≥ 48.41666666666666
Approximately,
x ≥ 48. 4 sets of knives
In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives
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Tolong bantuin makasih
Answers
Answer:
hello im ur friend and im going to give u the answer next year
What is the simplest form of the product 3 sqrt 4x^2.
Answers
We can use the radical rules to simplify the product 3(4x2). To start, we simplify 4 to its square root, which equals 2. Next, we employ the power property of radicals, which asserts that (a,m) = (a(m/2)), to simplify the cube root (x2) by using it. In this instance, (x2) = x.
We now get 3 * 2 * x, which simplifies to 6x when the simpler terms are combined.The result is that the product 3(4x2) has the simplest form (6x).We can dissect the constituent parts and use the radical-simulation principles to simplify the product 3(4x2).In the beginning, we may reduce the square root of 4 to 2: 3(2x2).Then, since it contains a square (2) and a cube root (), we can reduce them as follows:
3 * 2 * x^(²/³)Taking the square root before the cube root is shown by the exponent 2/3. We may calculate the exponent by reducing it to: 3 * 2 * x(2/3)The terms are then combined when we multiply the coefficients: 6 * x(2/3)As a result, 6x(2/3) is the product of 3(4x2) in its simplest form.
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please help (due in 8 minutes!! have a blessed day/night)
Answers
Answer:
13
Step-by-step explanation:
\(--› \: \: \:3x + \frac{1}{4} {y}^{2} \)
Insert values
\(--› \: 3(3) + \frac{1}{4} {4}^{2} \)
multiply 3 by 3
\(--› \: 9 + \frac{1}{4} {4}^{2} \)
follow PEDMAS of operation
Calculate exponents 4\({}^{2}\)
\(--› \:9 + \frac{1}{4} \times 16\)
divide 16 by 4
\(--› \: 9 + 4\)
add 9 to 4
\(--› \: 13\)
Find the distance between points B and N.
B
N
+
-2.5
.5
-0.5
0.5
1.5
25
Answers
Answer:
see my questions and join
• N = -1
• B <-> N = 0.5
line b passes through points (-20, 4) and (-21, 96). line c is parallel to line b. what is the slope of line c?
Answers
The slope of the line c is - 92.
The points via which the line b passes are:
(-20, 4) and (-21, 96).
The slope of the line is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Slope of the line b passing through these points are:
m = (96 - 4) / (- 21 + 20)
m = (92) / (-1)
m = - 92
Since, line b is parallel to line c,
Slope of line b = slope of line c
So, the slope of line c is also:
m' = - 92
Therefore, we get that, the slope of the line c is - 92.
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2d²y/dx² + yd²y/dx² = 0, dy/dx at x = 0 = 0, dy/dx at x = infinite = 1, dy/dx at x = 5 = 0.99 d²z/dx² + k/2y dz/dx = 0 z(0) = 0 and z(infinite) = 1 k is just a constant. Solve the differential equations with boundary conditions. By using Runge kutta4 method with MATLAB
Answers
Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).
The resulting plot will show the solution curve.
To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.
Let's define new variables:
y = y(x)
z = dz/dx
Now, we have the following system of first-order differential equations:
dy/dx = z (1)
dz/dx = -k/(2y) (2)
To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.
The general formula for the fourth-order Runge-Kutta method is as follows:
k₁ = h f(xn, yn, zn)
k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)
k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)
k₄ = h f(xn + h, yn + k₃, zn + l₃)
yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6
zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6
where f(x, y, z) represents the right-hand side of equations (1) and (2).
We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:
function [x, y, z] = rungeKuttaMethod()
% Parameters
k = 1; % Constant k
h = 0.01; % Step size
x0 = 0; % Initial x
xn = 10; % Final x (adjust as needed)
n = (xn - x0) / h; % Number of steps
% Initialize arrays
x = zeros(1, n+1);
y = zeros(1, n+1);
z = zeros(1, n+1);
% Initial conditions
x(1) = x0;
y(1) = 0;
z(1) = 0;
% Runge-Kutta method
for i = 1:n
k1 = h * f(x(i), y(i), z(i));
l1 = h * g(x(i), y(i));
k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);
l2 = h * g(x(i) + h/2, y(i) + k1/2);
k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);
l3 = h * g(x(i) + h/2, y(i) + k2/2);
k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);
l4 = h * g(x(i) + h, y(i) + k3);
y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;
z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;
x(i+1) = x(i) + h;
end
% Plotting
plot(x, y);
xlabel('x');
ylabel('y');
title('Solution y(x)');
end
function dydx = f(x, y, z)
dydx = z;
end
function dzdx = g(x, y)
dzdx = -k / (2*y);
end
% Call the function to solve the differential equations
[x, y, z] = rungeKuttaMethod();
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What are 10 multiples of 3?.
Answers
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
Given that,
We have to find the 10 multiples of 3.
We know that,
What is multiple?We can find the multiples of a number by counting the digits. A multiple in mathematics refers to the outcome or output of multiplying two numbers together.
The Least Common Multiple is the smallest common multiple of two or more numbers (Least Common Multiple).
The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Therefore, The 10 multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 when we can just write the table of 3 all terms.
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Evaluate each of the following. help plz
Answers
Answer:
5!= 120
13!= 6227020800
12!/6!= 665280
10!/7! 3!= 120
5(4!)= 120
Step-by-step explanation:
Can someone pls help me with this
Answers
Answer: Question 1 is 62
Question 2 is 52
Step-by-step explanation:
Answer:
questions 1 is
questions 2 is 52
What is the range of the data set?{12, 10, 10, 8, 6, 7, 7, 12) ?
1
5
6
Answers
Answer: 6
Step-by-step explanation:
The range of a data set is the difference between the highest and lowest value. To solve this math problem, we will first find the highest and lowest value in the set.
1. Look at the data set: {12, 10, 10, 8, 6, 7, 7, 12}
2. To find the highest value, look for the largest number. The highest number in the set is 12.
3. To find the lowest value, look for the smallest number. The lowest number in the set is 6.
4. To calculate the range, subtract the lowest value from the highest value. 12 - 6 = 6
5. The range of the data set is 6.
A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
Answers
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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Question 41 of 50What are the restricted values forOA. I0OB. y0C. x 0, y = 0OD. no restrictions3ry²4y÷ 2²?3y
Answers
If we simplify the quotient of algebraic expressions we get the following:
\(\frac{3xy²}{4y}\div\frac{2x²}{3y}=\frac{9xy³}{8x²y}=\frac{9y²}{8x}\)therefore, the restriction is x different of 0
Last year a tree was 12.8 meters tall it grew 1.35 meters taller this year if it grows the same amount next year how tall will the trees be
Answers
Answer:
15.5 meters tall
Step-by-step explanation:
Add 1.35 for each year to the start amount.
You work as a market researcher for a company that delivers products ordered through the Internet. You want to know the proportion of orders that arrive on-time. Based on a random sample of recent customers, you find that the 95% confidence interval for the proportion of all orders arriving on-time is 0.88 ± 0.06. Which of the conclusions listed below is correct?
Group of answer choices
a. On 95% of the days people ordered products, between 82% and 94% of the orders will arrive on time
b. Between 82% and 94% of all orders arrive on time
c. We are 95% sure that between 82% and 94% of orders arrive on time
d. We are 95% sure that between 82% and 94% of the orders placed by the sampled customers arrive on time
e. Ninety-five percent of all random samples of customers will show that 82% to 94% of the orders arrive on time
Answers
The correct conclusion is c. We are 95% sure that between 82% and 94% of orders arrive on time.
Let's analyze each conclusion:
a. On 95% of the days people ordered products, between 82% and 94% of the orders will arrive on time.
This conclusion is not supported by the given information. The confidence interval is based on the proportion of orders arriving on time, not the proportion of days. It doesn't provide information about the percentage of orders that arrive on time on specific days.
b. Between 82% and 94% of all orders arrive on time.
This conclusion is not supported by the given information. The confidence interval represents an estimate for the proportion of orders arriving on time, not the range of all orders. It only provides information about the likely range of proportions for the entire population based on the sample.
c. We are 95% sure that between 82% and 94% of orders arrive on time.
This conclusion is correct. The confidence interval indicates that we can be 95% confident that the true proportion of all orders arriving on time falls within the range of 82% to 94%. It represents the likely range of proportions for the entire population of orders.
d. We are 95% sure that between 82% and 94% of the orders placed by the sampled customers arrive on time.
This conclusion is not accurate. The confidence interval is calculated based on the sampled customers and provides an estimate for the proportion of on-time orders for the sampled group. It does not provide information about the proportion of orders placed by the sampled customers, but rather the likely range of proportions for all orders in the population.
e. Ninety-five percent of all random samples of customers will show that 82% to 94% of the orders arrive on time.
This conclusion is not supported by the given information. The confidence interval represents the range of likely proportions for all orders, not the likelihood of obtaining similar intervals in future random samples of customers.
Therefore, the correct conclusion is c. We are 95% sure that between 82% and 94% of orders arrive on time.
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Y=-3x-1 find the solution
Answers
The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.
The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.
In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.
To find the solution to this equation, you would need to have a specific value for either x or y.
If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.
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In simple graphical method a graph is plotted from the available data, between water usage and population. 2) Pressure in a distribution system must be high enough to permit the fire department adequate hydrant flows. 3) Distribution system is used to describe collectively the facilities used to supply water from its source to the point of usage. 4) Brackish water or briny water is water that has more salinity than fresh water, and more than seawater salinity. 5) The effect of monthly variation influences the design of storage reservoirs. 6) Jordan is not considered a "Water Scarce" country. 7) If a fire breaks out, a small quantity of water is required to be supplied during long duration, necessitating the need for a maximum rate of hourly supply. 8) The Manning equation is commonly used to design and evaluate the performance of sanitary sewers. 9) If d is less than 200 mm then the pipe final diameter D is 200 mm. 10) The diameter for lateral pipe is larger than the diameter of interceptor pipe.
Answers
The given statements are correct or incorrect is given below:
1) Correct.
2) Correct.
3) Correct.
4) Correct.
5) Correct.
6) Incorrect.
7) Correct.
8) Correct.
9) Correct.
10) Incorrect.
Here, we have,
1) Correct. In a simple graphical method, a graph is plotted to show the relationship between water usage and population.
2) Correct. The pressure in a distribution system needs to be sufficient to allow for adequate hydrant flows in case of a fire.
3) Correct. The term "distribution system" refers to the infrastructure and facilities used to supply water from its source to the point of usage.
4) Correct. Brackish water is water that has a higher salinity level than fresh water and even higher than seawater.
5) Correct. Monthly variation in water usage can impact the design and capacity requirements of storage reservoirs.
6) Incorrect. Jordan is considered a "Water Scarce" country, as it faces significant challenges in terms of water availability and scarcity.
7) Correct. During a fire, a significant quantity of water needs to be supplied over an extended period, necessitating a high rate of hourly supply.
8) Correct. The Manning equation is commonly used in the design and evaluation of sanitary sewers.
9) Correct. If the diameter (d) is less than 200 mm, the pipe's final diameter (D) is set at 200 mm.
10) Incorrect. The diameter of the interceptor pipe is typically larger than the diameter of the lateral pipe. The interceptor pipe carries wastewater from multiple lateral pipes.
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Imagine you have ¼ of a pie to split with your friend. Explain how you would divide fractions to figure out how much of the pie each of you will have.
Answers
To divide fractions to figure out how much of the pie each of you will have, we can follow these steps:
Write the fraction that represents the amount of pie that each person will get. Let's call this fraction "x".
To divide a fraction, we need to multiply the first fraction by the reciprocal of the second fraction. In this case, we want to divide 1/4 by the number of people, which is 2. The reciprocal of 2 is 1/2.
Multiply the first fraction by the reciprocal of the second fraction. This gives us:
x = 1/4 ÷ 2
x = 1/4 × 1/2
Simplify the resulting fraction by multiplying the numerators and denominators:
x = (1 × 1) / (4 × 2)
x = 1/8
So each person will get 1/8 of the pie.
To divide fractions and split the pie, you would multiply your fraction (1/4) by the reciprocal of the total fraction (1/1), resulting in 1/4 for each person.
How would you divide fractions to determine the equal share of a pie if you have 1/4 of it to split with your friend?To divide fractions and divide the pie evenly between you and your friend, you would multiply your fraction (1/4) by the reciprocal of the total fraction representing the pie (1/1).
Multiplying fractions involves multiplying the numerators (1 * 1) and denominators (4 * 1) separately, resulting in 1/4. This means that each of you would receive 1/4 of the pie. This can be visualized as cutting the pie into four equal parts, and each person receiving one of those parts.
By dividing fractions, you are essentially dividing the whole into equal portions. In this case, the fraction 1/4 represents the equal portion of the pie that each person would receive.
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Let Y 1 ,Y2 and Y3 be independent and identically distributed random variables with expectation E[Yi ]=μ and variance V[Yi ]=σ 2
for i=1,2,3. Suppose we want to estimate the expectation μ, and we propose to combine our three observations Y 1 ,Y2 and Y3 by defining a weighted average: Yˉω =ω1 Y1+ω 2Y2 +ω3 Y3 where ω1 ,ω2 and ω3
are constants between 0 and 1 . 1 (a) Calculate E[ Y
ˉ
ω
]. What condition do the weights ω 1
,ω 2
and ω 3
need to satisfy for Y
ˉ
ω
to be an unbiased estimator for μ ? (b) Calculate V[ Y
ˉ
ω
]. Using the condition you found on (a), find the set of weights that minimize the variance of Y
ˉ
ω
. Justify your answer. Now suppose that observations Y 1
,Y 2
and Y 3
are independent and have the same mean μ, but they have different variances. Specifically, V[Y 1
]=V[Y 2
]=σ 2
and V[Y 3
]=2σ 2
Answers
a.) The weights, ω1 + ω2 + ω3 = 1. b.) The weights, V[Y_bar ω] = ω1²V[Y1] + ω2²V[Y2] + ω3²V[Y3] = ω1²σ² + ω2²σ² + ω3²σ² = σ²(ω1² + ω2² + ω3²). To estimate the expectation μ, we propose combining three independent and identically distributed random variables Y1, Y2, and Y3 using a weighted average, Y_bar ω = ω1Y1 + ω2Y2 + ω3Y3.
(a) The weights ω1, ω2, and ω3 need to satisfy the condition ω1 + ω2 + ω3 = 1 for Y_bar ω to be an unbiased estimator for μ. The expectation E[Y_bar ω] is calculated as E[Y_bar ω] = ω1E[Y1] + ω2E[Y2] + ω3E[Y3] = ω1μ + ω2μ + ω3μ = (ω1 + ω2 + ω3)μ. For Y_bar ω to be an unbiased estimator for μ, its expectation should equal μ. Therefore, ω1 + ω2 + ω3 = 1.
(b) The variance V[Y_bar ω] can be calculated as V[Y_bar ω] = V[ω1Y1 + ω2Y2 + ω3Y3]. Since Y1, Y2, and Y3 are independent, the variance of their sum is the sum of their variances. Therefore, V[Y_bar ω] = ω1²V[Y1] + ω2²V[Y2] + ω3²V[Y3] = ω1²σ² + ω2²σ² + ω3²σ² = σ²(ω1² + ω2² + ω3²). The variance of Y_bar(ω) can be calculated, and by applying the condition from (a), the set of weights that minimize the variance can be determined.
To minimize the variance, we can apply the condition from (a), ω1 + ω2 + ω3 = 1, and use a technique called Lagrange multipliers. By introducing the Lagrange multiplier λ, we form the Lagrangian L = σ²(ω1² + ω2² + ω3²) + λ(ω1 + ω2 + ω3 - 1). Taking partial derivatives with respect to ω1, ω2, ω3, and λ, we can solve the equations to find the set of weights that minimize the variance. The specific values will depend on the given values of σ² and the constraints imposed by the problem.
learn more about Lagrange multiplier here: brainly.com/question/30776684
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April rented a car for $14.20 per day plus $0.16 per mile. If her bill was
$42.68, how many miles did April drive in one day.
Answers
Answer:
178 miles
Step-by-step explanation:
We know that there is a constant of $14.20 that is the fee. This can represent b in our slope intercept formula. For every mile, the cost is 16 cents, which can replace m when x represents the number of miles driven.
y=mx+b
y=.16x+14.20
We know her entire bill is 42.68, so we can plug that in as y and solve for x.
42.68=.16x+14.20
Minus 14.20 from both sides
28.48=.16x
Divide both sides by .16
x=178
14.20+.16x=$42.68
-14.20 -14.20
.16x=28.48
*divide both sides by .16
ANSWER: 178 miles
Help me please I’ll give brainliest if your correct
Answers
To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:
x = -b/2a
where a = -5 and b = 286.
x = -b/2a
x = -286/(2(-5))
x = 28.6
So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).
Therefore, the widgets should be sold for $28.60 to maximize the company's profit.
Hope I helped ya...
Answer:
29 cents
Step-by-step explanation:
The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:
\(y=-5x^2+286x-2275\)
The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.
The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:
\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)
For the given equation, a = -5 and b = 286.
Substitute these into the formula:
\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)
\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)
\(\implies x_{\sf vertex}=\dfrac{286}{10}\)
\(\implies x_{\sf vertex}=28.6\)
Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.
Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.
