a) The power of the test for this two sided alternative is 0.684
b) We need a sample size of at least 716 from each machine to detect the difference with a probability of at least 0.9 and a significance level of 0.05.
The power of the test, denoted by 1 - β, where β is the probability of failing to reject the null hypothesis when it is actually false, can be calculated using the non-central standard normal distribution.
Using the given values, we have n1 = n2 = 300, p1 = 0.05, p2 = 0.01, α = 0.05, and δ = 0.04. Substituting these values into the formula, we can compute the power of the test as follows:
1 - β = P( Z > Z0.025 - 0.04√(n) / √( p (1 - p) (1/n1 + 1/n2) ) ) + P( Z < -Z0.025 - 0.04√(n) / √( p (1 - p) (1/n1 + 1/n2) ) )
where Z0.025 is the upper 0.025 quantile of the standard normal distribution, which is approximately 1.96.
We can estimate the pooled sample proportion as:
p = (x1 + x2) / (n1 + n2) = (15 + 8) / (300 + 300) = 0.0433
Substituting the values, we have:
1 - β = P( Z > 1.96 - 0.04√(300) / √(0.0433(1 - 0.0433)(1/300 + 1/300))) + P( Z < -1.96 - 0.04√(300) / √(0.0433(1 - 0.0433)(1/300 + 1/300)))
Solving this equation using statistical software or a calculator, we obtain 1 - β = 0.684.
Therefore, with the given sample sizes, the power of the test for the two-sided alternative hypothesis H1: p1 ≠ p2 is 0.684 when the significance level is 0.05 and the effect size is 0.04.
Moving on to part (b) of the question, we need to determine the sample size needed to detect the difference with a probability of at least 0.9 and a significance level of 0.05..
Substituting the values, we have:
n = (Z0.025 + Z0.90)² * (0.0433 * 0.9567 / 0.04²) ≈ 715.27 or 716
To know more about hypothesis here
https://brainly.com/question/29576929
#SPJ4
The total circular area a sprinkler can water is 240 2 . The sprinkler is set to rotate back and forth in a 75° pattern. Find the amount of area that will get watered.
Answer:
The sprinkler will cover an area of [tex]50m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 240m^2[/tex]
[tex]\theta = 75^{\circ}[/tex]
Required
Determine the amount of area it can cover
The amount of area is calculated by calculating the area of a sector using:
[tex]Sector\ Area =\frac{\theta}{360^{\circ}} * \pi r^2[/tex]
Where:
[tex]Area = \pi r^2 = 240m^2[/tex]
So, we have:
[tex]Sector\ Area =\frac{\theta}{360^{\circ}} * 240m^2[/tex]
Substitute 75 for [tex]\theta[/tex]
[tex]Sector\ Area =\frac{75^{\circ}}{360^{\circ}} * 240m^2[/tex]
[tex]Sector\ Area =\frac{75^{\circ}* 240m^2}{360^{\circ}}[/tex]
[tex]Sector\ Area =\frac{75* 240m^2}{360}[/tex]
[tex]Sector\ Area =\frac{18000m^2}{360}[/tex]
[tex]Sector\ Area =\frac{18000}{360} m^2[/tex]
[tex]Sector\ Area =50m^2[/tex]
Hence, the sprinkler will cover an area of [tex]50m^2[/tex]
Solve for a, 7-a=3 A.10 B.4 C.2 D5
Answer:
B
Step-by-step explanation:
7 - a + 3
subtract 7 from both sides.
-a = 3 - 7
add like terms (3 + - 7)
-a = -4
divide both sides by -1. (remember that in front of the a, a 1 is there.)
a = 4
answer: b. 4
I do not understand this at all
Answer:
2s+3b=154
s=2b
solving: s= 44, b= 22
Step-by-step explanation:
s=number of sundaes sold
b=number of banana splits sold
2s+3b=154
s=2b
to solve:
substitute s=2b into the first equation
2(2b)+3b=154
4b+3b=154
7b=154
divide both sides by 7
7b/7=154/7
b=22
s=44
The winning times for a race are shown in the table.
Which answer describes the rate of change from year 2 to year 4?
- The winning time increased by an average of 0.267 second per year from year 2 to year 4.
- The winning time increased by an average of 0.8 second per year from year 2 to year 4.
- The winning time increased by an average of 0.4 second per year from year 2 to year 4.
- The winning time increased by an average of 0.475 second per year from year 2 to year 4.
Answer: The winning time increased by an average of 0.4 second per year from year 2 to year 4.
The winning time for a race displayed in the table would be:
C). The winning time increased by an average of 0.4 seconds per year from year 2 to year 4.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Find the increase in winning time:
Given that,
Year Winning Time(seconds)
1 27.5
2 28.4
3 28.7
4 29.2
5 29.44
Hence, The total change in the time is,
= (0. + 0.3 + 0.5 + 0.24)/4
= 0.485 seconds
Now, If we round off, it becomes 0.5 seconds.
Therefore, it can be considered that an average of 0.5 seconds changes every year from year 2 to 4.
Thus, ''Option C'' is the correct answer.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
GameStop is going out of business and everything is 60% off. What is
the new price of a game that regularly costs $58.99?
Answer:
With original price $58.99 and 60% off,
Final price: $23.60
Saved amount: $35.39
Step-by-step explanation:
For 3/4 of a pound of peanuts, Jimmy paid $2.35. What is the unit rate (dollars per pound)? *
Answer:
$3.13/lb
Step-by-step explanation:
Divide 3/4 pound into $2.35:
$2.35
--------- = $3.13/lb
3/4 lb
Show set of data that is a function using at least 5 domain values and 5 range values. It can be shown in a format of your choice
Answer:
Five domain values of the function f(x) = x² - 1, are; 1, 2, 3, 4, 5
Five range values of the function f(x) = x² - 1, are; 0, 3, 8, 15, 24
Step-by-step explanation:
The values in the domain are the values of the independent or (normally) x-variable
The values i the range are the values obtained by applying the function relationship to the domain as follows;
Let 'f(x)' represent the function that generates the values of the data in the data set,
For f(x) = x² - 1, we have the following table;
[tex]\begin{array}{ccc}x&f(x)\\1&0\\2&3\\3&8\\4&15\\5&24\end{array}[/tex]
Therefore;
The function is f(x) = x² - 1
The five domain values are; 1, 2, 3, 4, 5
The five range values are; 0, 3, 8, 15, 24.
Susie bought 6 yards of fabric to make scarves. She estimates that it takes 3/5 yard to make huge scarf. How many scarves can Susie make?
please help me on this will give you brainliest
Answer:
57.603
Step-by-step explanation:
We can separate this into two sections, using the and:
Fifty-seven - simply the whole number 57
Six hundred three thousandths - This could be intrepreted as 0.603, which is confirmed through the "3" being in the thousandths place.
Sorry that took so long! I had to think a bit about this one
????????????????????????????
Answer:
Pretty sure it's c)
solve for x. -3(x+5)=-9
Answer:
x = -2
Step-by-step explanation:
Find the unit rate for this situation: type 145 words in 5 minutes
Answer:
29 words per minute
Step-by-step explanation:
[tex] \frac{145}{5} = 29 \\ \frac{29}{1} = 29[/tex]
Answer:
29 words per minute
Step-by-step explanation:
145/5 = 29 words per minute
Hope that helps!
6.please help this timed!!!
Answer:
X=2
Step-by-step explanation:
3x+y=11
(+)2x-y=-1 (Add so you get rid of the y's)
5x=10
5x/5=10/5
x=2
write the product using exponents
Answer:
11^5
Step-by-step explanation:
11^5 because your multiplying 11 by itself 5 times
What unit should be used to calculating fundraising for field trip
Answer:
the mcps i think
Step-by-step explanation:
Im not sure :/
Find the product of (x + 5)(x − 5). Group of answer choices x2 − 10x + 25 x2 + 10x + 25 x2 − 25 x2 + 25
First I will tell you the formula for this, then I will show how we got the formula, then the answer.
Formula -> (x+a)(x-a)=x^2-a^2
We can find this by expanding the 2 ( )
(x+a)(x-a)=x^2+ax-ax-a^2=x^2-a^2
Now we can use this to solve your problem, the 5 is the a in the formula.
(x+5)(x-5)=x^2-5^2=x^2-25. Therefore choosing the 3rd answer choice.
Evaluate the expression,
if x = 9, y = 14, and z = 6.
X•y-z2
Answer:
90
Step-by-step explanation:
6^2=36
9*14=126
126-36=90
Answer:
90
Step-by-step explanation:
X ° Y - z2 =
9 x 14 - 6 x 6 =
126 - 6 x 6 =
126 - 36 = 90
Bodmas is used for this equation, the order of the sums that you should do:
1. The sum in the bracket
2. Division
3. Multiplication
4. Addition
5. Subtraction
Do it left to right, you can do division and multiplication and addition and subtraction too but it's based on left to right.
Use the Distributive Property to rewrite the algebraic expression. 7(6m + 7)
wrong answers reported
Step-by-step explanation:
first, distribute 7 to 6m (this means 7 • 6m)
7 • 6m = 42m
then distribute 7 to 7 (which is 7 • 7)
7 • 7 = 49
your simplified expression is 42m + 49. i hope this helps! have a great day <3
(b) A circle has radius 26 cm and length of its chord is 48 cm. Find how far is the
chord from the centre of the circle?
Answer:
22cm
,,,,,,,,,,,,ፀ,,,,,,
Which is the simplified version of:
7x + 12 + 3x = -6 (x - 7) + 9x
A. 5x = -30
B. 7x = -54
C. 7x = 30
D. 7x = -19
PLEASE DON’T GUESS :(
Will mark brainliest if your rightƪ(˘⌣˘)ʃ
Answer:
The answer is letter D
Step-by-step explanation:
Answer:
7x+3x=10x
-6(x-7)= -6x+42
then 10x+12=-6x+42+9x
10x+12=3x+42
10-3=42_12
7x=30
then the correct answer is C
The image of the point (8,1) under a translation is (9,2). Find the coordinates of
the image of the point (5,5) under the same translation.
1-2-3-4-5-6-7-8-9-10
0.10)/%
Please help me 3x+y=-3
Answer:
x=0 y=-3
Step-by-step explanation:
solve this please for me
Answer:
c is answer plz see the pic it's the solution
re-write the equation in Ax+By=C form. use integers for A,B, and C.
y+2=-5(x-5)
Answer:
5x+y=23
Step-by-step explanation:
y+2=-5(x-5)
y+2=-5x+25
y=-5x+25-2
y=-5x+23
23=y-(-5x)
23=y+5x
5x+y=23
The width of a rectangle is 7 inches and the length is 13 longer than the width. Find the perimeter of the rectangle. (PLEASE ANSWER QUICKLY!!!)
A cereal box has a length of 9 inches, a width of 3 inches, and a height of 13 inches. What is the volume of the cereal box?
Answer:
351 is the answer to how much volume a cereal box has
Answer:
352
Step-by-step explanation:
all you do is multiply 9×3×13
plz help!!!! i’ll mark brainliest!!
Lorenzo tiene 4 cajas de huevo, cada uno con 50 huevos y 3 cartones del mismo producto con 10 de ellos ¿Cuántos huevos hay en total?
Responder:
240 huevos
Explicación paso a paso:
Número de cajas de huevos = 4
Huevos por caja = 50
Total de huevos en caja = 50 * 4 = 200 huevos
Número de cajas = 3
Número de huevos por caja = 10
Total de huevos en caja = 10 * 4 = 40 huevos
Huevos totales = (huevos en caja + huevos en cartón)
Total = (200 + 40) = 240 huevos
What statement is true for life insurance coverage?
O A. The policy only covers beneficiary's future needs, funeral costs should not be included in the
policy amount
B. Debt is forgiven at death, so insurance policies do not need to cover this cost.
O
C Life insurance policy amounts should factor in how much it would take to maintain the standard
of living for the beneficiaries
D. Generally speaking, $10,000 is the recommended amount for a life insurance policy
Answer:
C: Life insurance policy amounts should factor in how much it would take to maintain the standard of living for the beneficiaries
Step-by-step explanation:
The statement is true for life insurance coverage
Life insurance policy amounts should factor in how much it would take to maintain the standard of living for the beneficiaries.
What is Life insurance coverage?A contract between an insurance policy holder and an insurance company in which the insurer agrees to pay a quantity of money in exchange for a premium upon the demise of an insured person or after a specific amount of time is known as life insurance.
In order to provide a death benefit in exchange for paying premiums, life insurance functions. One common kind of life insurance, called term life insurance, only lasts for a predetermined period, such 10 or 20 years. Although the death benefit of permanent life insurance likewise lasts during the policyholder's lifetime as long as premiums are paid, it does not.
Thus, the true statement is
Life insurance policy amounts should factor in how much it would take to maintain the standard of living for the beneficiaries.
Learn more about Life insurance coverage here:
https://brainly.com/question/9611644
#SPJ2
What is the simplified form of this expression? (-3x2 + x + 5) − (4x2 − 2x) A. 7x2 + 3x − 5 B. -7x2 + 3x + 5 C. X2 − x + 5 D. -x2 + 3x − 11