We have calculated a confidence interval based on a sample of size n=474. If we want to have a new margin of error that is only one third as large, we need to change the sample size to ____________ (Assume that the other quantities are not affected by the change of the sample size).
Answers
The new sample size needed to achieve a margin of error that is one-third as large would be 53.
To find the new sample size needed to achieve a margin of error that is one third as large, we can use the formula for the margin of error in a confidence interval:
Margin of Error = Z * (Standard Deviation / √n)
Where Z is the z-score corresponding to the desired confidence level, Standard Deviation is the population standard deviation, and n is the sample size.
Since we want the margin of error to be one third as large, we can set up the following equation:
(Z * (Standard Deviation / √n)) / 3 = Z * (Standard Deviation / √n')
Where n' is the new sample size.
Simplifying the equation, we can cancel out the Z and Standard Deviation terms:
√n' = √n / 3
Squaring both sides of the equation, we get:
n' = n / 9
Therefore, the new sample size needed to achieve a margin of error that is one-third as large is one ninth (1/9) of the original sample size.
So, the new sample size would be n / 9 = 474 / 9 = 52.67 (rounded up to the nearest whole number).
Therefore, the new sample size needed would be 53.
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Related Questions
(2x-3y)(x+5y)=0 where x>0 and y>0
Find the ratio x:y
Give your answer in its simplest form.
Answers
Answer: \(3:2\)
Step-by-step explanation:
Using the zero-product property, we know that \(2x-3y=0\) or \(x+5y=0\). We can rearrange these cases to yield \(x=\frac{3}{2}y\) and \(x=-5y\).
However, since \(x\) and \(y\) have the same sign, we neglect the case \(x=-5y\). This means \(x=\frac{3}{2}y\).
\(x=\frac{3}{2}y \implies \frac{x}{y}=\frac{3}{2} \implies x:y=3:2\)
Answer: We can use the distributive property to expand the left side of the equation:
2xx + 2x5y - 3yx - 3y5y = 0
Then, combine like terms:
2x^2 + 10xy - 3xy - 15y^2 = 0
Now we can add 3xy + 15y^2 on both sides of the equation to get:
2x^2 + 10xy = 0
We know that x and y are positive, so we can divide both sides by 2:
x^2 + 5xy = 0
and since x>0, we can divide both sides by x:
x + 5y = 0
So the ratio x:y = x/(-5y) = -x/5y.
To simplify we can divide x by -x and 5y by 5y and get the final answer as
x:y = -1:
Step-by-step explanation:
An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Polsson distribution, then the probability of renting exactly three apartments in a week is ....
Answers
The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.
The probability of renting exactly three apartments in a week is given by the Poisson probability function:
\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)
Substituting the values, we get:
\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)
P(X = 3) = (0.09963 * 12.167) / 6
P(X = 3) = 0.2018
Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.
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Albert wrote a total of 5 pages of his essay in 2 hours. How many hours will Albert need to complete a 12 page paper?
Answers
Answer:
Step-by-step explanation:
…
Explanation: 5 / 2 is 2.5 so thats the amount of pages per hour. 12 / 2.5 is 4.8
in a bag of marbles 4 are
blue. 5 are white, and 11 are
red. What is the probability of
NOT drawing a red?
Answers
Answer:
3/4 or a 75%
Step-by-step explanation:
What is the volume of a cylindrical garbage pail with a radius of 10 centimeters and a height of 50 centimeters?
Answers
Answer:
500\(\pi\) or around 1570
Step-by-step explanation:
The formula for a volume of a cylinder is \(r^{2}h\pi\)
The cylindrical garbage pain has a volume of 15700 cm².
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
The given cylindrical garbage has a radius(r) = 10 cm and a height(h) of
50 cm.
∴ The volume of the cylindrical garbage is = π(10)²×50 cm².
= 5000π cm².
= 15700 cm².
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Find the side of to cube
whose volume is
5.832cm3
Answers
Answer:
\(1.8cm\)
Step-by-step explanation:
Use the volume of cube formula.
\(\displaystyle V=s^3\)
\(\displaystyle5.832=s^3\)
\(\displaystyle\sqrt[3]{5.832} =s\)
\(\displaystyle s=1.8\)
Answer:
a= 1.8 cm
Step-by-step explanation:
V= a³
a= ∛Va= ∛5.832a= 1.8 cmThe apothem of a circle is 10.5 cm. Find the area.
Answers
Solution
The given apothem is 10.5cm
The area the circle will be calculate as
\(\pi\cdot(10.5)^2\)Therefore the area of the circle is:
\(346.36cm^2\)pls help asap!!! Find the value of z
Answers
What type(s) of symmetry does the letter "D" have?
Reflectional
Rotational
Point
Identity are the options.
Answers
—————————————————————————
The letter "D" exhibits reflectional symmetry about a horizontal mirror because when these letters are rotated 180 degrees clockwise or anticlockwise the letters appear to be the same.
Rotational Symmetry is the property a shape has when it looks the same after rotation as it did at its starting point.
Given that,
The letter D is given.
Since the letter 'D' has one line of symmetry and is rotated 180 degrees clockwise or anticlockwise the letters appear to be the same.
Hence, The letter "D" exhibits reflectional symmetry about a horizontal mirror.
So, the correct option is,
''Reflectional''
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PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS THANKS
Answers
Answer:
1/6
Step-by-step explanation:
Hope it helps you in your learning process
Answer:
the second one
Step-by-step explanation:
1/6
brainliest pls
What is the slope of the line passing through (-3, 2) and (-1, -1)
Answers
m= -1-2/-1-(-3)
m= -3/2
Therefore slope is -3/2
y+1=3(x-4)y+1=3(x−4) find the slope
Answers
Answer:
0
y+1= (3x-12)y+1=3x-12
given that z is a standard normal variable, p(z > 1.61) is (rounding to two decimal places):
Answers
The probability that a standard normal variable z is greater than 1.61 is 0.0549.
This is derived from the standard normal table which gives the area under the normal curve between -∞ and the given value.
This area is equal to the probability of the variable falling between -∞ and the given value. For a standard normal variable, the area between -∞ and 1.61 is 0.9451, which is the probability of the variable falling between -∞ and 1.61.
The area between 1.61 and ∞ is 0.0549, which is the probability of the variable falling between 1.61 and ∞.
Therefore, the probability of z being greater than 1.61 is 0.0549.
Complete Question:
Given that z is a standard normal variable, what is the probability that z is greater than 1.61?
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у
80
The graph of quadratic function
is shown on the grid.
What is a solution to r(x) = 0?
60
40
A -50
20
B 4
х
-4
4
8
12
- 16 -12 -8
16
C 14
-20
D-60
vo
-60
-80
Answers
Answer:
C 14
Step-by-step explanation:
(8.1 x 104)
+
(2.5 x 104). Express your answer in scientific notation.
Answers
Answer:
=10.6x104
Step-by-step explanation:
=8.1x104+2.5x104
=(8.1x104+2.5x104)
=10.6x104
(8.1 x104)+(2.5 x 104)
Multiply the numbers
842.4 + (2.5 x 104)
Multiply the numbers
842.4 +260
Now we do the same thing only different way
2
2.5
x 104
________
100
000
2 50 0
______________
260
Multiply the digits
4 x 5 =20
Take the last digit and write it in the answer line
Carry the next digit and save it for the next calculation
Multiply the digits
4 x 2=8
Add the carried digit for the previous result
8+2 =10
Write the result in the answer line
Move the next digit and write it the next result below
Every digit multiplied by zero equals zero
Move to the next digit an write the next result below
Every digit multiplied by one stays the same
Add the numbers
Move the decimal sign as many times as there are decimal places in both factors combined.
Remove the unnecessary zeros
The result is 260
842.4+260
Add the numbers
1102.4
842.4
+ 260.0
_________
1102.4
Write zeros to get the same number of decimal places.
Add the digits in the column
4+0=4
Write the result under the column
Add the digits in the column
2+0=2
Solution: 1102 .4
Alternate form : 5512/5 , 1102 2/5
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helen wants to test the level of comfort of a new recliner compared to the old model. she creates two equivalent groups through random sampling, has the control group sit in the old model, and has the other group sit in the new one. afterward, she has members of each group rank comfort level based on their experience of sitting in the recliner, on a scale of 1 to 5. this is an example of a
Answers
On a scale of 1 to 5, Helen asks each group's members to rate their level of comfort while sitting in the recliner. An illustration of a "posttest-only design" is this.
Define the term posttest-only design?A research design known as the posttest-only comparison group involves at least two groups, each of which does not undergo a treatment or intervention.
Data are then gathered on the outcome measure following the treatment or an intervention. The control group is the one who doesn't get the desired treatment or intervention.This design's general procedure is as follows:
two or more groups are created; the treatment is delivered; information is gathered after the delivery of the treatment or intervention, typically using a psychological assessment; as well as the results are compared among groups to ascertain out whether treatment was successful.As per the question-
Helen wants to compare the new recliner's comfort level to that of the previous one.
Through random selection, she establishes two equivalent groups, places the control group in the pre-existing model, and places the other group in the post-existing model.
Following that, she asks participants in each group to rate their level of comfort on the a scale of 1 to 5 depending on experience sitting in a chair.
Thus, an illustration of such a "posttest-only design" is this.
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A carton of grapefruit juice displays the nutritional information shown below. How many grams of sugar are there in a 200 ml glass of juice? Grapefruit juice 250 ml contains Carbohydrate Sugar Protein 19.5 g | 16.5 g | 1.5 g
Answers
Answer:
13.2 g
Step-by-step explanation:
let x = grams sugar in a 200 ml glass
16.5 g sugar / 250 ml = x g sugar / 200 ml
x(250) = (16.5)(200)
x = (16.5)(200) / (250) = 3300 / 250 = 13.2
Answer: there are 13.2 g sugar in a 200 ml glass of juice
A simple random sample of 10 items resulted in a sample mean of 25. The population standard deviation is = 8. Round your answers to two decimal places. a. What is the standard error of the mean, o? 2.
Answers
Therefore, the standard error of the mean, σ= 2.53 (approx).
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.
Given: A simple random sample of 10 items resulted in a sample mean of 25.
The population standard deviation is = 8.
We have to find out the standard error of the mean, σ/Sample Size n,
so we will first calculate σ as;
σ = Population standard deviation = 8
Sample Size n = 10
Substituting values in the formula to find the standard error of the mean, we get;σ/√n = 8/√10 = 2.53 (Round off the value to two decimal places)
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Which of the expressions below will have a remainder? Select all that apply.
A) 733÷4
B) 384÷3
C) 296÷5
D) 819÷2
Answers
Answer:
a , c , d
Step-by-step explanation:
Answer:
Fwee pointz, wite? bc ppl already answered XD it from over a week ago too
Step-by-step explanation:
Use the drop-downs to identify the domain and range of the following relation.
{(4, -7), (0, 6), (5,-3), (5, 2)}
What is the domain of this relation?
What is the range of this relation?
Answers
Answer:
Domain ( -4,0, 5) Range ( -7, -3, 2, 6)
Step-by-step explanation:
The domain and range of the given relation {(4, -7), (0, 6), (5,-3), (5, 2)}
is:
Domain = { 4, 0, 5, 5 }
Range = { -7, 6, -3, 2 }
Given,
{(4, -7), (0, 6), (5,-3), (5, 2)}
We need to find what is the domain and range of this relation.
What are the domain and range of a function?A function has an input and an output.
Example: f(x) = x + 4
Now,
x = 1, 2, 3
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
Here,
Domain = 1, 2, 3
Range = f(1), f(2), f(3) = 5, 6, 7
We can also write it as { (1,5), (2,6), (3,7)}
Find the relation.
(4, -7)
Here,
domain = 4 and range = -7
(0, 6)
domain = 0 and range = 6
(5,-3)
domain = 5 and range = -3
(5, 2)
domain = 5 and range = 2
Find the domain and range of {(4, -7), (0, 6), (5,-3), (5, 2)}.
Domain = { 4, 0, 5, 5 }
Range = { -7, 6, -3, 2 }
Thus the domain and range of the given relation {(4, -7), (0, 6), (5,-3), (5, 2)}
is:
Domain = { 4, 0, 5, 5 }
Range = { -7, 6, -3, 2 }
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tom worked for 80 min how long did tom work
Answers
Answer:
80 minutes
Step-by-step explanation:
Answer:
Tom worked for 1 hour and 20 minutes.
Step-by-step explanation:
what is the total number of people who have the disease? group of answer choices 60/115 60 60/95 55 30 35 175 25
Answers
The total number of people who have the disease is 115.
The total number of people in the sample population is
Total = 175
The negative predictive value is
NPV= (TN / (TN + FN)) = (25 / (25 + 55) = 25 / 80 = 0.3125
The positive predictive value
PPV = (TP / (TP + FP)) = (60 / (60 + 35) = 60 / 95 = 0.6316
The sensitivity of the test
Sensitivity = (TP / (TP + FN)) = (60 / (60 + 55) = 60 / 115 = 0.5217
The total number of people who have the disease
= 60+55 = 115
The number of False Positives (FP)
= 35
The number of True Positives (TP)
= 60
The total number of people that tested negative
= 80
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solve for xxx. reduce any fractions to lowest terms. don't round your answer, and don't use mixed fractions. 54x 64 \geq 49x 5954x 64≥49x 59
Answers
The inequality 54x/64 ≥ 49x/59 simplifies to x ≥ 0. Thus, the solution for x is greater than or equal to zero.
To solve the inequality 54x/64 ≥ 49x/59, we can begin by cross-multiplying:
(54x)(59) ≥ (49x)(64)
3186x ≥ 3136x
Next, we can subtract 3136x from both sides:
3186x - 3136x ≥ 0
50x ≥ 0
Finally, we divide both sides by 50:
x ≥ 0/50
x ≥ 0
Therefore, the solution to the inequality is x ≥ 0.
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Are these equations equivalent? 4x-12y=16 and 2x-6y=8
Answers
Answer: yes
Step-by-step explanation:
the 2nd can be reached by dividing it by 2
Answer:
Below.
Step-by-step explanation:
Yes, because if we divide the first one by 2 we get the second equation:
4x/2 - 12y/2 = 16/2
= 2x - 6y = 8
Select the methodology that would result in a subjective probability....
Dividing the number of favorable events by the number of possible events.
Studying the fraction of times in the past a particular event has happened.
Weighing the available information and assigning a probability.
Answers
Weighing the available information and assigning a probability.
A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.
So, as per the definition of subjective probability
Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus
Weighing the available information and assigning a probability.
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Eliana got a new puppy for her birthday. She went to the pet store to buy what
she needed for the puppy: a food dish for $7.95, a leash for $9.95, a collar for
$6.95, a crate for $29.90, a bag of food for $10.98, and a chew toy for $2.50.
What is Eliana's total including sales tour of the sales tax rate is 8.25% ?
Answers
Answer: 5.628975
Step-by-step explanation:
Add everything up to get $68.23
A radioactive isotope is decaying at a rate of 18% every hour. Currently there
are 120 grams of the substance.
Write an equation that will represent the number of grams, y, present after
hours.
=
Can you tell me the answer please
Answers
The decay of the radioactive substance can be modeled by the exponential decay function:
y = a(1 - r)^t
where:
- y is the amount of substance present after t hours
- a is the initial amount of substance (in grams), which is 120 grams in this case
- r is the decay rate per hour, which is 18% or 0.18 in decimal form
- t is the time elapsed in hours
Plugging in the values we get:
y = 120(1 - 0.18)^t
Simplifying:
y = 120(0.82)^t
So this is the equation that represents the number of grams, y, present after t hours, given the initial amount of 120 grams and a decay rate of 18% per hour.
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The frequency table shows the results of tossing a ball 24 times into the four coloured sections on a carnival game Section | number of | Tosses Blue | 3 Green | 5 Red | 12 Yellow | 4 Based on the data on the table, how many times will the ball most likely land in the yellow section when it is tossed 200 times? A. 35 B. 40 C. 50 D. 65
Answers
Answer:
50
Step-by-step explanation:
you toss the ball 24 times, and of those 24 times, it lands 12 times on the yellow section, so 12/24= 0.5
Answer: 50
Step-by-step explanation:
GEOMETRY HW: Two dogs are swimming after a ball that was thrown in a pond as shown in the figure. To the nearest tenth, how far from the ball is Molly?
Answers
Answer:
someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Step-by-step explanation:
Answer:
its B
25.4 ft
Step-by-step explanation:
a family has two children. m represents male, and f represents female.what is the sample space for the gender of the children?
Answers
MM, MF, FM, and FF where MM stands for two boys, MF stands for one boy and one girl in that order, FM stands for one girl and one boy in that order, and FF stands for two females.
As per the question given,
The sample space for the gender of the children consists of all possible combinations of the genders of the two children. Assuming that the gender of each child is independent of the other and equally likely to be male or female, the sample space can be represented as:
{MM, MF, FM, FF}
where MM represents two boys, MF represents one boy and one girl in that order, FM represents one girl and one boy in that order, and FF represents two girls.
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