Answer:
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex[ or 98%
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p_1[/tex] represent the real population proportion for 1
[tex]\hat p_1 =0.768[/tex] represent the estimated proportion for 1
[tex]n_1=92[/tex] is the sample size required for 1
[tex]p_2[/tex] represent the real population proportion for 2
[tex]\hat p_2 =0.646[/tex] represent the estimated proportion for 2
[tex]n_2=95[/tex] is the sample size required for 2
[tex]z[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:
[tex]ME= \frac{0.2753-(-0.0313)}{2}=0.1533[/tex]
And we know that the margin of erro is given by:
[tex]ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
We have all the values except the value for [tex]z_{\alpha/2}[/tex]
So we can find it like this:
[tex]0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}[/tex]
And solving for [tex]z_{\alpha/2}[/tex] we got:
[tex]z_{\alpha/2}=2.326[/tex]
And we can find the value for [tex]\alpha/2[/tex] with the following excel code:
"=1-NORM.DIST(2.326,0,1,TRUE)"
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex] or 98%
The confidence level is 95%. This conclusion is reached by converting the upper bound of the confidence interval into a standard z-score and comparing it to the z-scores for common confidence levels.
Explanation:To determine the confidence level of interval, we need to look at the proportion of the total area under the standard normal curve that falls within the interval when converted into a standard z-score. For instance, a 90% confidence interval corresponds to an area of 0.90 under the curve, with 0.05 in each tail, and a Z score of ±1.645. A 95% confidence interval corresponds to an area of 0.95 under the curve, with 0.025 in each tail, and a Z score of ±1.96. A 99% confidence level corresponds to an area 0.99 under the curve, with 0.005 in each tail, and a Z score of ±2.575.
In this case, with a confidence interval of (-0.0313, 0.2753) and the estimated proportions of p1=0.768 and p2=0.646, we find the estimated difference is 0.122 and its standard deviation is 0.0782.
Converting the upper bound of the confidence interval into a standard z-score: (0.2753 - 0.122) / 0.0782 = 1.959, which corresponds to a 95% confidence level. Thus, the inference can be that if we were to sample from these populations many times, in 95% of the cases, the true difference between p1 and p2 would lie within the interval (-0.0313, 0.2753).
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In one country, residents were asked to name their primary language. The ratio of residents who said French to those who said Punjabi was 110 to 7. If there 7,260,000 residents who said French, about how many thousands of residents said Punjabi?
Answer:
462000
Step-by-step explanation:
here,let the punjabi be x
110/7=7260000/x
110x=7260000*7
x=462000
Answer: 462
Step-by-step explanation: I had the question and it said it was 462
What is the slope of the line that passes through (-3, 2) and (1, 2)?
Answer:
0
Step-by-step explanation:
Slope of a line which passes through two points (x1,y1) and (x2,y2) is given by:
\frac{y2-y1}{x2-x1}
(x1,y1) = (-3,2)
(x2,y2) = (1,2)
Substituting the values in the equation to determine the slope of the line:
= \frac{2-2}{1-(-3)}
= \frac{0}{4}
=0
So the slope of the given line is 0.
This is intuitively evident as well as the y coordinates of the two given points are the same.
If the mix ratio for certain chemical is 1:6 when it is mixed with water (chemical:water), how much water would be mixed with 1/2 gallon of the chemical?
Answer:3 gallons of water would be mixed with 1/2 gallon of the chemical
Step-by-step explanation:
If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.
Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes
1/2 × 6 = 3 gallons of water.
Answer: 3 gallons of water would be mixed with 1/2 gallon of the chemical
Step-by-step explanation:
If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.
Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes
1/2 × 6 = 3 gallons of water.
The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)?
Answer:
39 feet.
Step-by-step explanation:
E use the Pythagoras theorem:
40^2 = 8^2 + h^2 as h is the height we require.
h^2 = 1600 - 64
h^2 = 1536
h = 39.19 feet
Kylo bought a pizza for $12.75 and four medium drinks at Pauli's Pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink cost $3.
Answer:
Step-by-step explanation:
Let d be the cost of a drink. The expression for the cost of the pizza and 4 drinks is
12.75 + 4d
If each drink costs $3, then
12.75 + 4(3) simpifies to
12.75 + 12 which equals 24.75
If quadrilateral WXYZ is inscribed in a circle with center O, the measure of angle W = 45 and the measure of angle X = 110, then the measure of angle Z = _____.
Check the picture below.
Mary is consuming at a point on her budget line. Her income is $40 a week, and she purchases hamburgers and grilled cheese sandwiches. If both goods cost $2 each, and she purchases five hamburgers, how many grilled cheese sandwiches does Mary buy?
Answer:
Mary buy $30 / $ 2 = 15 grilled cheese sandwiches
Step-by-step explanation:
five hamburgers cost 42 x 5 = $10
money left for grilled cheese sandwiches = $40 - $ 10 = $ 30
each grilled cheese sandwiches cost $2
Mary buy $30 / $ 2 = 15 grilled cheese sandwiches
Sleepy is eight years younger than scoopy. Doc is 5 times as old as scoopy. The sum of their age is 55. How old are each of them? This is the exact problem from worksheet.
Answer:
The age of Sleepy is 1 .
Then the age of Scoopy is 9.
The age of Doc would be 45.
Step-by-step explanation:
We have to find the ages of all the three people based on the given equations.
Let the age of Sleepy be x. Since Scoopy is 8 years older than Sleepy, the age of Scoopy would be (x+8).
Also Doc is 5 times as old as Scoopy so his age is 5(x+8).
Now the sum of the ages of all three is 55.
Writing equation for this,
x + x + 8 + 5(x+8) = 55
7x + 48 = 55
7x = 7
x = 1
So the age of Sleepy is 1 .Then the age of Scoopy is 9.
The age of Doc would be 45.
By solving the linear equations given by the problem, it is found that Scoopy is 10 years old, Sleepy is 2 years old, and Doc is 50 years old.
Explanation:This problem is a system of linear equations, a topic in the field of mathematics. The task is to find out the age of Sleepy, Scoopy, and Doc. Let's denote Scoopy's age as 'S', Sleepy's age as 'S - 8' (since Sleepy is eight years younger than Scoopy), and Doc's age as '5S' (since Doc is 5 times as old as Scoopy). The equations can be written as below:
Scoopy's age = SSleepy's age = S - 8Doc's age = 5SIt is known that the sum of their ages is 55, which gives us our second equation:
S + (S - 8) + 5S = 55
By solving this equation, we find that S = 10. So Scoopy is 10 years old. Accordingly, Sleepy is 10 - 8 = 2 years old and Doc is 5 * 10 = 50 years old.
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There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter the first coin is a nickel, the second is a dime and the third is a quarter
Answer:
The question is incomplete, this is the complete question.;
There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter the first coin is a nickel, the second is a dime and the third is a quarter.find the probability of this occurring.
The answer to the question is;
the probability of this occurring is 1/27
Step-by-step explanation:
Let n(N) =5 ( the number of nickels)
n(D) =5 ( the number of dimes) and
n(Q) = 5 ( the number of quarters)
P(N)= 5/15=1/3 (prob of picking a nickel)
P(D) =5/15=1/3 (prob of picking a dime)
P(Q) = 5/15= 1/3 (prob of picking a quatre)
The probability of picking the three= P(N)×P(D)×P(Q)
= 1/3×1/3×1/3
= 1/27
A department store purchases a dress for $80. To sell the dress to customers, the price is marked up by 19%. You hand the clerk $110. How much change will you get back?a. $30.00b. $15.20c. $95.20d. $14.80
Answer:
Amount returned will be $14.80
So option (D) will be correct answer
Step-by-step explanation:
We have given the purchase price of store = $80
To sell the dress price is marked up by 19 %
So marked up price [tex]=80+\frac{80\times 19}{100}=$95.2[/tex]
He give the $110 to clerk
We have to find the amount which is returned by clerk
So the amount will be equal to $110-$95.2 = $14.8
So option (d) will be correct answer
If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k ?
Answer:
any digit 0 to 9
Step-by-step explanation:
Nothing about your description of the number suggests that the 10s digit depends on the units digit. The tens digit can be any digit 0 to 9.
Over the course of four weeks Mia spent 35 1 2 hours training for a race. Michael spent 1 1 2 times that amount training for the same race. How many hours did Michael spend training? A) 49 1 2 hours B) 53 1 4 hours C) 71 hours D) 73 1 4 hours
Answer:Michael spent 53 1/4 hours
training.
Step-by-step explanation:
Over the course of four weeks Mia spent 35 1 2 hours training for a race. This can be written in decimal point as 35.5 hours.
Michael spent 1 1 2 times that amount training for the same race. Converting 1 1 2 to decimal, it becomes 1.5 hours.
This means that the number of hours that Michael spent training will be 35.5 × 1.5 = 53.25 hour.
Converting 53.25 hours to mixed fraction, it becomes
53 1/4 hours
Answer:
The answer is B
Step-by-step explanation:
Sam watched television the past five nights for 42 minutes, 23 minutes, 56 minutes, 19 minutes, and 67 minutes. What was the median amount of time Sam watched TV the past five nights?
Answer:
42 minutes is the median amount of time
Step-by-step explanation:
The Median is the middle value of data set.
If there is "odd" number of numbers, and there are n numbers, the median is:
(n/2) + 1 th number
If there is "even" number of numbers, and there are n numbers, the median is:
Average of n/2th and (n/2) + 1 th number
Here, we have 5 numbers, so the median would be:
(5/2) + 1 th number
That is
3rd number
But, we need to arrange the numbers from least to greatest. Lets write it:
19, 23, 42, 56, 67
The third number is 42, this is the median
Help plz... I forgot how to find the angles...can someone tell me how to do it por favor...y
gracias
Answer: a=70°
b=45°
c=65°
d=45°
e=70°
f=110°
Step-by-step explanation:
a=70°
b=180°-135°=45°
c=180-(70+45)=180-115=65°
c=65°
e=70°
d=180-(c+e)=180-(65+70)=180-135=45°
d=45°
f=180-e=180-70=110°
If you assume that there are exactly 365 days in a year, how many seconds are there in one year? Give your answer to the nearest 1000 seconds.
Answer:
31,536,000
Step-by-step explanation:
There are 3600 seconds in an hour and 24 hours in a day, so ...
(3600 s/h)(24 h/da) = 86400 s/da
Then in 365 days, there are ...
(365 da)(86400 s/da) = 31,536,000 s
_____
No rounding is needed.
There are 31,536,000 seconds in a year. This is calculated by multiplying 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year.
Explanation:To calculate the number of seconds in a year, start with the known values of time:
There are 60 seconds in 1 minute,60 minutes in 1 hour,24 hours in one day,and 365 days in one year (for this question, we're ignoring leap years).
We multiply all these values together to get the number of seconds in a year.
60 seconds/minute * 60 minutes/hour * 24 hours/day * 365 days/year = 31,536,000 seconds/year
To give the answer to the nearest 1000 seconds, we would round it to 31,536,000.
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Neural networks, fuzzy systems, and evolutionary computation are all forms of __________, where systems develop intelligence through an iterative learning process.a. relational intelligenceb. conventional intelligencec. fuzzy logicd. computational intelligence
Answer:
d. computational intelligence
Step-by-step explanation:
Neural networks, fuzzy systems, and evolutionary computation are all forms of computational intelligence, where systems develop intelligence through an iterative learning process.
Computational intelligence (CI) is a machine intelligence which usually refers to the ability of a computer to learn or perform a specific task from data or experimental observation. This implies the systems have the ability to learn and generalize from examples and develop intelligence through an iterative process. Computer intelligence is also known as soft computing. The major Computational intelligence are Fuzzy logic, Neural networks and Evolutionary Computing. Presently, Computational Intelligence is an evolving field. New additions are evolving in addition to the three major CI. These new CI include soft computing like artificial endocrine networks, artificial life, ambient intelligence, cultural learning and social reasoning.
Neural networks, fuzzy systems, and evolutionary computation contribute to the field of computational intelligence, demonstrating adaptive learning capabilities and continuous improvement. Option d) is the correct answer.
Neural networks, fuzzy systems, and evolutionary computation are all forms of computational intelligence, where systems develop intelligence through an iterative learning process. Concepts such as evolution and adaptation, which originate in evolutionary biology, stretch to the domain of complex systems involving the development of adaptive, non-biological processes that have dynamic learning and creative abilities.
These systems are part of artificial intelligence, where computer systems learn from data to improve over time. These forms of artificial intelligence have been rapidly developing since the 1980s and are often associated with machine learning, suggesting a broad category where systems can adapt, process information, and optimize problems.
Calculate the area of an isosceles right triangle who's hypotenuse is 42–√ inches.
Answer:
A = 441 in²
Step-by-step explanation:
An isosceles right triangle is a triangle with two equals sides (the legs ). In this particular case the base of the triangle will be the length of one side and at the same time the height of the triangle will be the other leg. Hypotenuse as always is the opposite side to the right angle.
The area of a triangle is
A = (1/2) * b* h
If we are going to compute the area of such triangle we have to find the length of one side That will be the base of the triangle and at the same time that will be the height of the triangle.
In any right triangle hypotenuse is:
H² = L₁² + L₂² (1)
As was explain before in this particular case L₁ = L₂
Then
H² = L₁² + L₁² ⇒ H² = 2 L₁² H = √2 * L₁ ⇒ L₁ = 42/√2
Then area of the
A = (1/2)* ( 42/√2) * ( 42/√2 ) ⇒ A = 1/4 * (42)²
A = 441 in²
The final agreed-to sample size is a trade-off between acceptable error and research cost.
Answer:
True
Step-by-step explanation:
Sample size selection is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is important in any empirical statistical study in which the goal is to make inferences about a population from a sample. The actual sample size used in a study is determined based on the time money and technical cost of data collection, and the need to have sufficient statistical accuracy.
Finding a balance between acceptable error and research cost gives rise to concepts like Confidence Interval and Margin of Error.
The taylor family brought 6 suitcases with them on their trip to italy. They paid $72 to check their luggage in with the airport. What was the cost for each piece of luggage
Answer:
$12
Step-by-step explanation:
72/6=12
Each of the suitcases cost 12 dollars and in total, all 6 suitcases equated to 72 dollars.
Answer: the cost for each piece of luggage is $12
Step-by-step explanation:
The total number of suitcases that the Taylor family brought on their trip to Italy is 6. They paid $72 to check their luggage in with the airport. Therefore, the cost for each piece of luggage would be
Total amount paid for 6 pieces of luggage divided by the total number of pieces of luggage. It becomes
72/6 = 12
How did New World colonization, enabled by the vessel above, affect the economy of Europe?
Answer:
The New world colonization enabled by the vessel affect the European economy as it increased the amount of gold and silver brought into Europe, this lead to the development of the banking sector and also helped to promote the transition of Europe into a capitalist economy.
it brought a great deal of gold and silver into Europe, stimulating the banking industry and promoting Europe’s transition of capitalism
On august 1st, a plant was 79 centimeters tall. in june of that year it grew 12 centimeters, then 9 more centimeters in july. how many centimeters tall was it on june 1st?
a.67
b.70
c.100
d.5
Answer: d. 58
The height of the plant in June 1st is 58 centimeters.
Step-by-step explanation:
Given : On August 1st, a plant was 79 centimeters tall.
In June of that year it grew 12 centimeters, then 9 more centimeters in July.
Order of Month = June → July → August
Then , the height of the plant on June 1st would be
Height in August 1st - Height grew in June - height grew in July
= 79-12-9 centimeters
= 67-9 centimeters
= 58 centimeters
Therefore , the height of the plant in June 1st = 58 centimeters
Hence, the correct answer is d. 58
Simplify the expression.
1-cot x / tan x-1
A) cot x
B) tan x
C) -cot x
D) csc x
Answer:
The answer to your question is letter A) cot x
Step-by-step explanation:
[tex]\frac{1 - cot x}{tan x - 1}[/tex]
Remember that cot x = [tex]\frac{1}{tan x}[/tex]
Then
[tex]\frac{1 - \frac{1}{tan x} }{tanx -1}[/tex]
Simplify
[tex]\frac{\frac{tan x - 1}{tan x} }{tan x - 1}[/tex]
[tex]\frac{tan x - 1}{tan x (tan x - 1)}[/tex]
[tex]\frac{1}{tan x}[/tex]
Result
[tex]\frac{1}{tan x} = cot x[/tex]
Jackson sells two types of toolboxes. He plans on selling them during a farming fair this weekend. He estimates he will sell 20 of the smaller boxes and 12 of the larger boxes. If he'd like the profit to be $1300, which of the following best displays the equation that represents this information?
A. y = −5/3x + 325/3 ~~
B. 20x + 12y = 1300
C. y + 12 = 20(x–1300)
D. 12y = 20x – 1300
Answer:
B
Step-by-step explanation:
In this case, we use variables to represent the the cost of the big and the smaller boxes. Let x be the selling price of the big boxes while y be the selling price of the bigger boxes.
The total selling price of the smaller boxes is 20x. The total selling price of the bigger ones is 12y.
Now we know he is making a profit of $1,300
Hence in equation form, all the information above can be represented as:
20x + 12y = 1,300
On the track team, 35of the members are boys. Of these boys, 47 are sixth-graders. Of the sixth-grade boys on the team, 13 are runners. What fraction of the track team are sixth-grade boy runners?
Answer:
The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team .
Step-by-step explanation:
Given as :
The Total number of the member in team = x
The number of boys in team = [tex]\dfrac{3}{5}[/tex] of x
I.e number of boys in team = [tex]\dfrac{3 x}{5}[/tex]
Again
The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] of total boys in team
I.e The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] × [tex]\dfrac{3 x}{5}[/tex]
Or, The number of sixth-grade boys = [tex]\dfrac{12 x}{35}[/tex]
Again
The number of runners = [tex]\dfrac{1}{3}[/tex] of number of sixth-grade boys
i.e The number of runners = [tex]\dfrac{1}{3}[/tex] × [tex]\dfrac{12 x}{35}[/tex]
Or, The number of runners = [tex]\dfrac{4 x}{35}[/tex]
So, The number of runners = [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team
Hence,The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team . Answer
Which of the following triangles is closest to being right? Explain your reasoning.
Answer: Second triangle.
Step-by-step explanation:
For this exercise you need to use the Pythagorean Theorem. Based on it, you know that in a right triangle:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the right triangle and "b" and "c" are the legs.
In this case you can identify that the legs of the first triangle and the legs of the second triangle are equal. These are:
[tex]b=7\\c=3.3[/tex]
Knowing their values, you can substitute them into the Pythagorean Theorem and solve for "a":
[tex]a^2=(7)^2+(3.3)^2\\\\a=\sqrt{(7)^2+(3.3)^2}\\\\a=7.738[/tex]
Therefore, you can conclude that the triangle that is closest to being a right triangle is the second one.
Ernie calculated the slope between two pairs of points. He found that the slope between ( ( -1, 4) 1 , 4 ) and (0, 0) ( 0 , 0 ) is -4 4 . He also found that the slope between (2, 7) ( 2 , 7 ) and (3, 3) ( 3 , 3 ) is -4 4 . Ernie concluded that all of these points are on the same line. Use the drop-down menus to complete the statements about Ernie's conclusion.
Answer:
His conclusion was incorrect.
Step-by-step explanation:
Since, slope of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the slope between (-1, 4) and (0, 0),
[tex]m_1=\frac{0-4}{0+1}=-4[/tex]
Also, the slope between (2, 7) and (3, 3),
[tex]m_2=\frac{3-7}{3-2}=\frac{-4}{1}=-4[/tex]
Now,
There are two cases possible,
Case 1 : line passes through (-1, 4) and (0, 0) is parallel to line passes through (2, 7) and (3, 3)
Case 2 : (-1, 4), (0, 0), (2, 7) and (3, 3) are on the same line
Hence, we can not say that they are on same line only after getting same slope.
i.e. his conclusion was incorrect.
Answer:
Okay so this picture is basically the answer for anyone who needs it...
Step-by-step explanation:
Sajia has 30 books in her library she sold 9 books at a thrift store on Saturday write and solve an inquality to determine how many more books she can sell if she comes back on Sunday
Answer:
see the explanation
Step-by-step explanation:
Let
x ---->the number of books she can sell if she comes back on Sunday
y ----> the number of books sold on Saturday
we know that
The number of books sold on Saturday plus the number of books she can sell if she comes back on Sunday must be less than or equal to the initial number of books in the library (30 books)
so
The inequality that represent this situation is
[tex]x+y\leq 30[/tex]
we have
[tex]y=9\ books[/tex]
substitute
[tex]x+9\leq 30[/tex]
solve for x
subtract 9 both sides
[tex]x\leq 30-9[/tex]
[tex]x\leq 21\ books[/tex]
therefore
The maximum number of books she can sell on Sunday is 21
Estimate the quotient 430 divided by 9
Answer:
47.77778 but really it's just 47
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone? (1) Jack is painting twice as fast as Tom. (2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours.
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n
a. has the same probability of being selected
b. has a probability of 1/n of being selected
c. has a probability of n/(N-1) of being selected
d. has a probability of 1/N of being selected g
Answer:
a) has the same probability of being selected
Step-by-step explanation:
A simple random sampling means that each possible sample of size n has the same probability of being selected.
Then your answer is:
a) has the same probability of being selected
The definition of a simple random sampling method implies that each possible sample of a given size has an equally likely chance of being selected. Hence, option a. 'has the same chance of being selected' is the correct answer.
Explanation:The simple random sampling method is a statistical method used to select individual samples from a large population where each sample is given an equal chance of being selected. In a simple random sampling of size n from a finite population of size N, each possible sample of size n would have the same probability of being selected. Therefore, the correct answer is a. has the same probability of being selected.
It is crucial to note that the probability of a sample being selected is not dependent on its size (n) nor the total size of the population (N), as options b, c, and d suggest. Instead, it is determined solely by the sampling method, i.e., simple random sampling.
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