the following are the amount of time, in minutes, that it took a random sample of 20 technicians to perform a certain task: 18.1 20.3 18.3 15.6 22.5 16.8 17.6 16.9 18.2 17.0 19.3 16.5 19.5 18.6 20.0 18.8 19.1 17.5 18.5 18.0 assuming that the sample came from a symmetric continuous distribution, use the sign test at the 0.05 level of significance to test the null hypothesis that the mean of the population is 19.4 against a 2-sided alternative. perform the test using: (a) the binomial distribution; (b) the normal approximation to the binomial distribution.
Answers
The normal approximation to the binomial distribution is C ( n , r ) * p^r * q^n - r .
a )
the binomial distribution .
Null hypothesis H0: μ = 19.4
Alternative hypotheses H1: μ ≠ 19.4
19.4 with minus sign, we get
n = 20, x = 4 and n/2 = 10
Here x < n/2
Therefore, from table the computed P-Value is.
b )
the normal approximation to the binomial distribution ,
P = 2P(X ≤ 4 when θ = 1/2 )
= 2 (0.0059)
= 0.0118
Hence the P value, 0.0118, is less than 0.05, the null hypothesis must be rejected, and we conclude that the mean of the population is not 19.4 minutes.
Learn more about the hypothesis here:
https://brainly.com/question/17173491
#SPJ4
Related Questions
Shane plans on finding a summer job so he can earn enough money to buy a new laptop that costs $595. He has already saved $150. If Shane
finds a summer job that pays him $7.50 an hour after taxes are withheld, what is the minimum number of hours he will have to work in order to
purchase the laptop?
80
79
60
59
Answers
Answer:
59
Step-by-step explanation: x=number of hours
150+7.50x=595
7.50x=595-150
7.50x/7.50=445/7.50
x=59
2-period production economy: Economy has two periods, = 0,1. There is a
representative household and a representative firm. Household utility is given as
U(Co,C1) = log(Co)+ß log(C1) where ß E (0,1) is a discount factor. Firm production
function is given as F(K,L) = K«L1-a, where a € (0,1) is a capital share. Household is
endowed with initial level of capital K o in period O and maximum labor hours L= 1 in
each period += 0,1. Firms rent capital and hire labor every period and maximize their
profit.
(a) Write down Household's problem
(b) Write down Firm's problem
(c) Write down market clearing conditions
(d) Write down Social Planner's Problem
(e) Define Competitive Equilibrium
(f) Solve Social Planner's Problem: Show your steps to solve it
(g) Solve Competitive Equilibrium: Show your steps to solve it(h) Write down First
Welfare Theorem. Does the theorem hold? Verify it.
(i) Write down Second Welfare Theorem. Does the theorem hold? Verify it.
Answers
The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.
(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:
Max U(Co, C1) = log(Co) + ß log(C1)
subject to the budget constraint:
Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,
where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.
(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:
Maximize F(K, L) - RK - WL,
where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.
(c) The market clearing conditions are:
Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.
Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.
(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:
Maximize U(C0, C1) + F(K, L) - RK - WL,
subject to the production function F(K, L) and the market clearing conditions.
(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:
Household's problem is solved optimally.
Firm's problem is solved optimally.
Market clearing conditions hold.
(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:
L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],
where λ1, λ2, and λ3 are the Lagrange multipliers.
(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.
(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.
(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.
To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.
For more such question on production. visit :
https://brainly.com/question/2292799
#SPJ8
The fraction Four-thirteenths is the sum of Three-thirteenths and which fraction?
Answers
Answer:
as below
Step-by-step explanation:
\(\frac{4}{13}\) = \(\frac{3}{13}\) + \(\frac{x}{13}\)
Because the denominators are all the same.. just do normal math on top... in the numerator... so 1 /13 is your answer
Alicia records the total number of points scored in two games by 10 players on her basketball team.
28, 13, 4, 8, 15, 10, 22, 7, 11, 15
which box plot represents the data
Answers
The first option in the second row, Option(C) represents the data.
In order to solve the problem,
First, we need to arrange the numbers in ascending order.
4, 7, 8, 10, 11, 13, 15, 15, 22, 28
Median = 11+13/2
= 12
From the first range ( 4,7,8,10,11 ) , we can find Q1 also known as first quartile where Q1 = 8 ( middle-most number).
Similarly, from the second range ( 13,15,15,22,28 ) , we can find Q2 also known as third quartile where Q3 = 15 (middle-most number ).
Now, for the box plot,
We need to draw a number line from 0 to 32.
Next, we need to draw a box from Q1 to Q3 with a vertical line through the median.
Next, we put dots above 4 and 28 since our numbers start from 4 and end with 28.
Finally we join the dots and the box plot with a straight line.
Hence, option C is the correct choice.
To know more about Box plot:
https://brainly.com/question/27849170
#SPJ4
Olivia invested $2,400 in an account paying an interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550?
Answers
Answer:
8.7 so either 8 or 9 tenth of a year
Step-by-step explanation:
Is it compounded per month? I assume
1. Compound interest formula
FV = PV(1+r/100k)^kn
FV is the future value,
PV is the present value,
n is the number of years,
k is the number of compounding periods per year
r% is the nominal annual rate of interest
2. Plug in numbers
3550 = 2400(1+4.6/100*12)^12*n
71/48 = (6023/6000)^12n
12n = logBase(6023/6000)*(71/48)
n = answer/12
n ≈ 8.70
Can you explain how to do this?
Answers
Answer:
a) missing y-values: 4, 8
b) correct: y-intercept = 1
c) y = 2^x
Step-by-step explanation:
a)You complete the table by reading point values from the graph. You have already correctly filled the y-values for x=0 and x=1. The y-value at x=2 is 4. The y-value at x=3 is off the chart, but we expect it to follow the same pattern: it will be 2×4 = 8.
The table values are (x, y) = (0, 1), (1, 2), (2, 4), (3, 8).
__
b)The y-intercept is the point where the graph crosses the y-axis: (0, 1). You have correctly identified 1 as the y-intercept.
__
c)The equation for the curve will be an exponential of the form ...
y = a·b^x
The value of 'a' is the y-intercept: 1.
The value of 'b' is the ratio of successive y-values when x increases by 1.
b = 2/1 . . . for x=1 and x=0
The equation will be ...
y = 1·2^x
y = 2^x . . . . . simplified
Two of the angles in a triangle measure 41° and 61° What is the measure of the third angle?
Answers
Answer:
78 degrees
Step-by-step explanation:
All inner angles of a triangle make a sum of 180 degrees. Given 41 and 61 add up to 102, that leaves 78 degrees left to make 180
Y0UR M0MWY 100KS L1KE TH1$
Answers
Answer:
nks
Step-by-step explanation:
tha
A pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. What is the direction of the pedestrian's resultant vector? Hint: Draw a vector diagram. Ө 0 = [ ? ]° Round your answer to the nearest hundredth
Answers
First, let's represent the westward displacement with a vector pointing to the left and labeled as 7.4 km. Then, we can represent the southward displacement with a vector pointing downward and labeled as 9.2 km.
To find the resultant vector, we need to connect the tail of the first vector (westward displacement) to the head of the second vector (southward displacement). The resultant vector represents the combined effect of both displacements.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
Resultant magnitude = √(7.4^2 + 9.2^2) ≈ 11.7 km
Next, we can determine the direction of the resultant vector using trigonometry. The angle (Ө) between the resultant vector and the westward direction can be found using the inverse tangent:
Ө = arctan(9.2/7.4) ≈ 51.33°
Rounding to the nearest hundredth, the direction of the pedestrian's resultant vector is approximately 51.33° south of due west.
1. x+1 when x=10
2. 5y-8 when y=6
3. 6t-9m when t=5 and m=3
4. 62/2 when x=10
5. 5h3-3j2+20 when h=4 and j=5
Answers
Answer:
1
X is equal to 10
10 plus 1 equals 11
2
y is equal to 6
30 minus 8
is equal to 22
3
m equals 3 and t equals 5
30 minus 27
is equal to 3
4 not written properly
5 not written properly
Please answer with steps
{0.4), (-4,-6)
Answers
\((0.4), (-4,-6)\)
The LCM of a, b is the smallest multiplier that is divisible by both a and b
\(= 0.4(-4, -6)\)
What is the volume of a cylinder with base radius 4 and height 5?
Answers
Answer:
hey
Step-by-step explanation:
yep
Answer:
251.33
Step-by-step explanation:
formula of volume of cylinder is v=bh or V=πr2h
value of radius and height is given, so use V=πr2h
and calculate.
(-3,7), (5,11) what is the slope and can u show me how u got it please
Answers
Answer:
The formula for the slope is:
\(\frac{y_2-y_1}{x_2-x_1}\)
Assign each given point to a variable:
(x₁, y₁) = (-3, 7)(x₂, y₂) = (5, 11)Substitute in the values into the formula:
\(\frac{y_2-y_1}{x_2-x_1}=\frac{11-7}{5-(-3)}=\frac{4}{8} =\frac{1}{2}\)
Therefore, the slope is 1/2.
Answer:
1/2
Step-by-step explanation:
The formula for slope: \(\frac{y^2-y^1}{x^2-x^1}\)
Plug in:
\(\frac{11-7}{5-(-3)}\)
11 - 7 = 4
5-(-3)
5 + 3 = 8
4/8 = 1/2
The slope is 1/2.
Hope this helped.
alan wishes to construct a 95% confidence interval for the proportion of those testing positive for covid-19who require hospitalization. he wants the margin of error to be no more than 2%. what sample size is requiredif he uses a prior estimate of 15%.
Answers
Alan would need a sample size of at least 447 to construct a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, using a prior estimate of 15%.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
To find the sample size required for constructing a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, we can use the following formula:
n = [(z-score)² * p * (1-p)] / (margin of error)²
where:
n is the sample size
z-score is the critical value for a 95% confidence interval, which is 1.96
p is the prior estimate of the proportion, which is 0.15
margin of error is 0.02
Plugging in the values, we get:
n = [(1.96)² * 0.15 * (1-0.15)] / (0.02)²
n = 446.25
Rounding up to the nearest whole number, we get a required sample size of 447.
Therefore, Alan would need a sample size of at least 447 to construct a 95% confidence interval for the proportion of those testing positive for COVID-19 who require hospitalization with a margin of error no more than 2%, using a prior estimate of 15%.
To learn more about statistics from the given link:
https://brainly.com/question/28053564
#SPJ4
what is the volume of the figure. answer plz.
Answers
Answer:
Volume: 37.692 cm3
Step-by-step explanation:
1) 1/3 x 3.14 x 3 power of 2 x 4
2) 1.047 x 9 x 4
3) 37.692 cm3
Answer:
\(Volume ~of~cone=\pi /3r^{2} h\)
\(r=3cm\)
\(h=4 cm\)
\(volume=\pi /3\times3^{2} \times4\)
\(=12\pi =12\times3.14\)
\(=37.68~ cm^{2}\)
-----------------------
hope it helps...
have a great day!!
A ski instructor recorded the amount of snow that fell each Saturday during ski season. He displayed the data in a line plot.
What is the range in this set of data?
Answers
the range in this set of data is 25 inches. To find the range of snowfall amounts, we need to look at the line plot and identify the highest and lowest amounts of snowfall that were recorded.
The range in a set of data is the difference between the maximum and minimum values in the set.
To find the range of snowfall amounts, we need to look at the line plot and identify the highest and lowest amounts of snowfall that were recorded.
Let's say that the highest amount recorded was 30 inches and the lowest amount recorded was 5 inches. Then the range would be:
range = highest amount - lowest amount
range = 30 - 5
range = 25
Therefore, the range in this set of data is 25 inches.
Learn more about data here
https://brainly.com/question/14893265
#SPJ1
Help what is the value
Answers
Answer:
I love you 3566267840 and pas 123456
You borrow $30,000 to buy a car. The loan is to be paid off in 10 equal quarterly payments at 6% interest annual interest rate. The first payment is due one quarter from today. What is the amount of each quarterly payment (rounded)? A. $1,777. B. $2,803. C. $3,253. D. None of the above.
Answers
The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).
To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.
Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.
Learn more about Whole number here: brainly.com/question/19161857
#SPJ11
Which of the following is the Inverse of y = 3x?
a) f-1(x) = 1/3x b) f-1(x) = 3x c) f-1(x) = 3/x d) f-1(x) = x/3
Answers
The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.
To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.
The given function is y = 3x.
To find its inverse, let's swap x and y:
x = 3y
Now, solve this equation for y:
Dividing both sides of the equation by 3, we get:
x/3 = y
Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.
Among the given options:
a) f^(-1)(x) = 1/3x
b) f^(-1)(x) = 3x
c) f^(-1)(x) = 3/x
d) f^(-1)(x) = x/3
The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.
To know more about Inverse relationship.
https://brainly.com/question/31358458
#SPJ11
Negative sixteen plus the quotient of a number and 2 is 35.
Answers
If negative sixteen plus the quotient of a number and 2 is 35, the number is 102.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = x
Negative sixteen plus the quotient of a number and 2 is 35.
This can be written as,
Quotient of a number and 2.
x ÷ 2 = M (quotient)
So,
-16 + M = 35
Now,
Solve for M.
M = 35 + 16
M = 51
Now,
x ÷ 2 = 51
x/2 = 51
x = 51 x 2
x = 102
Now,
We can cross-check.
-16 + 51 = 35
35 = 35
Thus,
The number is 102.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
a square has an area of 49 square inches. if the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. find the dimensions of the rectangle.
Answers
Answer:
length = 9 in
width = 5 in
Step-by-step explanation:
Algebraic equations and solving:First find the side of square from the given area.Frame the expression for length and width with the help of the side of square.Frame the equation for finding the area of rectangle.Now, by solving the equation, we can find the dimensions of the rectangle.Area of square =side * side
Side² = 49
Side = √49
= 7 inches
Let the measurement added to the length and removed from the width be 'x'.
length = (7 + x) in
width = (7 -x )in
Area of rectangle = length *width
length * width = 45 square inches
(7 + x)(7-x) = 45
{Identity: (a + b)(a -b) = a² - b² where a = 7 & b = x}
7² - x² = 45
49 - x² = 45
-x² = 45 - 49
-x² = - 4
x² = -4 ÷ (-1)
x² = 4
x = √4
x = 2
Dimension of the rectangle:
length =7 + 2 = 9 in
width = 7 - 2 = 5 in
1
Find the arc length of the partial circle.
Either enter an exact answer in terms of it or use 3.14 for
a and enter your answer as a decimal.
units
Answers
Answer:
1.57 u
Step-by-step explanation:
The given figure is a quadrant of a circle . So , the circumference of the quadrant of a circle is ,
→ C = 2πr/4
→ C = πr/2
→ C = 3.14 × 1 /2
→ C = 1.57 units
Hence the required answer is 1.57 u .w is directly proportional to u if w=5 when u=3,find u when w is =2/7
Answers
Answer:
u = 6/35
Step-by-step explanation:
w = k * u
w = ku
Where
k = constant of proportionality
if w=5 when u= 3
w = ku
5 = k * 3
5 = 3k
k = 5/3
find u when w is =2/7
w = ku
2/7 = 5/3 * U
2/7 = 5/3u
u = 2/7 ÷ 5/3
= 2/7 × 3/5
= (2*3)/(7*5)
= 6/35
u = 6/35
Let v =leftanglebracket 8, negative 1 rightanglebracket. what is the approximate direction angle of v?
Answers
To find the approximate direction angle of vector v = ⟨8, -1⟩, we can use trigonometry and the inverse tangent function (arctan). Therefore, the approximate direction angle of vector v is approximately -0.1244 radians or -7.12 degrees.
The direction angle (θ) of a vector can be calculated using the formula:
θ = arctan(y/x)
where (x, y) are the components of the vector.
For the given vector v = ⟨8, -1⟩, we have x = 8 and y = -1.
θ = arctan((-1)/8)
Using a calculator or a mathematical software, we can evaluate this expression to find the approximate direction angle:
θ ≈ -0.1244 radians or approximately -7.12 degrees.
To learn more about vector click here: https://brainly.com/question/24256726
#SPJ11
What's 7/81 rounded to the nearest tenth?
Answers
Answer:
Did you mean 7.81 'cause if so-
the rounded answer would be 8.0
Step-by-step explanation:
If m H= 68°, what is HI to the nearest tenth? Show your work.
Answers
Answer: HI = 5.3 cm
Let HI = x
GH = 2cm
m< H = 68 degrees
to find HI, we will need to apply the SOH CAH TOA RULE
HI = hypotenus
GH = adjacent
Cos 68 = adjacent / hypotenus
Cos 68 = 2 / x
Cross multiply
2 = x * cos 68
cos 68 = 0.3746
2 = x * 0.3746
Isolate x
x = 2/0.3746
x = 5.3cm
Therefore, HI is 5.3cm
Write 117mm cubed as a fraction of 0. 7 cm cubed
Answers
Expression as a fraction of 0.7 cm³ for 117 mm³ is given by the fraction 0.117 / 0.7.
To write 117 mm³ as a fraction of 0.7 cm³,
we need to convert the units so they match.
Since there are 10 millimeters in a centimeter
1 cm = 10 mm
This implies,
1 cm³ = (10 mm)³
= 1000 mm³
Now we can express 117 mm³ as a fraction of 0.7 cm³:
117 mm³ / 0.7 cm³
To convert mm³ to cm³, we divide by 1000,
117 mm³ / 1000 = 0.117 cm³
Now we can express it as a fraction,
0.117 cm³ / 0.7 cm³
Simplifying the fraction, we divide the numerator and the denominator by 0.117,
= (0.117 cm³ / 0.117 cm³) / (0.7 cm³ / 0.117 cm³)
= 1 / (0.7 / 0.117)
To divide by a fraction, we multiply by its reciprocal:
= 1 × (0.117 / 0.7)
= 0.117 / 0.7
Therefore, 117 mm³ is equal to the fraction 0.117 / 0.7 when expressed as a fraction of 0.7 cm³.
Learn more about fraction here
brainly.com/question/10354322
#SPJ4
random variation that occurs in any time series is called what? part 2 a. seasonal patterns b. irregular component c. cyclical effects d. trends
Answers
The random variation that occurs in any time series is called the irregular component.
What is the term for the unpredictable variation in a time series?The irregular component refers to the random fluctuations or unpredictable patterns that are observed in a time series. It represents the unexplained variability in the data that cannot be attributed to any identifiable pattern, such as seasonal patterns, cyclical effects, or trends. It is often characterized by short-term fluctuations that occur randomly and do not follow a specific pattern or trend.
Learn more about variation
brainly.com/question/17287798
#SPJ11
can you please help me i need all the help i can get
Answers
Answer:
175
the error in the diagram is that it implies Elena read 1/5 of the book, not Andre
Step-by-step explanation:
x= total number of pages
A = 1/5*x
E = A+20 = 1/5*x+20
1/5*x + 20 = 55
1/5*x = 35
x = 35*5 = 175
I need to know what the answer to this is in radical form √6⋅√11⋅√5
Answers
Answer:
√330
Step-by-step explanation:
The product of radicals is the radical of the product.
(√6)(√11)(√5) = √(6·11·5) = √330
__
This cannot be simplified, because there are no square factors.