A friend of yours was interested in computing a confidence interval for the mean student debt accumulated by NC State graduates during their undergraduate education. They collected a random sample of 40 students, and asked each how much student debt they had; all responded and responded honestly. A histogram of the data indicated it was normally distributed. They computed a 95% confidence interval of ($36,400, $41,650). However, they were unsatisfied with the margin of error, wanting a more precise interval. Referring to their ST 311 notes, they noted that in order to reduce the margin of error by half, they needed to increase their sample size by a factor of 4. So, they collected another random sample of 160 students and found another 95% confidence interval, which was much narrower, having a margin of error of $1,318. They are satisfied with the precision of the confidence interval, but are a little confused : it’s not quite half the original margin of error. Explain why the margin of error wasn’t quite reduced by a factor of 0.5. Be specific.
Answers
Answer:
Explained below.
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean is:
\(CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\)
The margin of error for this interval is:
\(MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\)
The factors affecting the MOE are:
The sample size (n) is inversely proportional to the MOE, thus increasing n decreases the MOE and vice-versa. Variance (σ²) is the square of S.D. So if we increase σ² then σ increases. Since σ is directly proportional to MOE, increasing σ increases MOE. The confidence level is the value of (1 – α). If we increase the confidence level then the critical value increases and thus MOE also increases.Since the population standard deviation is not provided it is obvious the sample standard deviation is used to estimate the value of σ.
On increasing the value of σ the MOE will also increase.
As the sample size is inversely proportional, increasing the sample size by a factor of 4 will reduce the margin of error by half. But since σ is also increasing there are two factors affecting the MOE together.
Therefore reducing the MOE by more than half the original value.
Related Questions
which is the CORRECT answer choice?A.B,C OR D?This is a self-check activity
Answers
Given:
\(3\times2\begin{bmatrix}{-2} & {3} & {0} \\ {-4} & {2} & {6} \\ {6} & {-5} & {6}\end{bmatrix}\)Simplify,
\(\begin{gathered} 3\times2\begin{bmatrix}{-2} & {3} & {0} \\ {-4} & {2} & {6} \\ {6} & {-5} & {6}\end{bmatrix}=6\begin{bmatrix}{-2} & {3} & {0} \\ {-4} & {2} & {6} \\ {6} & {-5} & {6}\end{bmatrix} \\ =\begin{bmatrix}{-2\cdot6} & {3\cdot6} & {0\cdot6} \\ {-4\cdot6} & {2\cdot6} & {6\cdot6} \\ {6\cdot6} & {-5\cdot6} & {6\cdot6}\end{bmatrix}\ldots\text{ By applying scalar multiplication} \\ =\begin{bmatrix}{-12} & {18} & {0} \\ {-24} & {12} & {36} \\ {36} & {-30} & {36}\end{bmatrix} \end{gathered}\)Answer: option B)
\(\begin{bmatrix}{-12} & {18} & {0} \\ {-24} & {12} & {36} \\ {36} & {-30} & {36}\end{bmatrix}\)A pet shelter had fifty -four puppies and another six weee brought in. If ten puppies a day were adopted, how long would it take for all of them to be adopted?
Answers
Answer: 6 weeks
6 weeks
Step-by-step explanation:
666
Write two decimals that are equivalent to the given decimal 3.400
Answers
Answer:
3.4 and 3.40
Step-by-step explanation:
The numbers mean the same thing
find the value of X.
(√32)²= (X+2)²+x
Answers
Answer:
Answer:x=−6.274917217635375,1.2749172176353745
Step-by-step explanation:
(3(2))2=(x+2)2+x12=x2+5x+4
Step 1: Subtract x^2+5x+4 from both sides.12−(x2+5x+4)=x2+5x+4−(x2+5x+4)−x2−5x+8=0
For this equation: a=-1, b=-5, c=7.999999999999998−1x2+−5x+8=0Step 2: Use quadratic formula with a=-1, b=-5, c=7.999999999999998.x=−b±b2−4ac2ax=−(−5)±(−5)2−4(−1)(8)2(−1)x=5±57−2x=−6.274917217635375,1.2749172176353745
What is the answer to this combination lock
Answers
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
What is the slope of the line?
Answers
Answer:
3/4
Step-by-step explanation:
1.5/2= 3/4
You are choosing between two health clubs club a offers membership for a fee of $13 plus a monthly fee of $28 club B offers membership for a fee of $19 plus a monthly fee of $27 after how many months will the total cost of each health club be the same? What will be the total cost for each club?
Answers
To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.
Let's assume the number of months is represented by 'x'.
For Club A, the total cost is given by:
Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)
For Club B, the total cost is given by:
Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)
To find the number of months when the total cost is the same, we set the two equations equal to each other:
$13 + $28x = $19 + $27x
Simplifying the equation, we get:
$28x - $27x = $19 - $13
$x = 6
Therefore, after 6 months, the total cost of each health club will be the same.
To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:
Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181
Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181
So, the total cost for both Club A and Club B will be $181 after 6 months.
For such more question on equation
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Fill in the blank with the correct answer choice. A ___________ has exactly one pair of parallel lines. a. square c. trapezoid b. parallelogram d. rectangle Please select the best answer from the choices provided A B C D
Answers
Answer: C
Step-by-step explanation:
The rest of the quadrilaterals provided have 2 pairs of parallel lines.
The choice is:
CExplanation:
The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.
Here's what a trapezoid looks like :
\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)
Hence, this makes C the correct choice.Suppose you are 5 feet 2 inches tall. Give your height in meters and centimeters
Answers
5’2 to m=1.58496m
The perimeter of a rectangular garden is 280 m.
If the length of the garden is 81 m, what is its width?
Answers
Answer:
59m
Step-by-step explanation:
280 =81+81 +w + w
280=162+2w
2w =280-162
w=118/2
w=59m
Please help i will give brainlest!
Answers
Answer:
6×1+9×1/10+4×1/100+7×1/1000
Step-by-step explanation:
simplify pls do fast
Answers
The sum of the decimal values given is 0.93
Simplifying the decimal values can be done thus :
0.36 + 0.57Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .
0.36*100 = 36
0.57*100 = 57
Adding the whole numbers :
__36
+_57
_____
__93
Dividing the sum by 100 to convert to an equivalent decimal value,
93/100 = 0.93Therefore, the required value is 0.93
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Point Tis on line segment SU. Given ST = 2 and TU = 15, determine the length
SU.
Answers
Answer:
SU = 17
Step-by-step explanation:
The line looks like this
S--T---------------U
If you add 2 + 15 = 17
Hope this helps ya!!
Drag & Drop: Order these rational numbers from least to greatest
Answers
Answer:
-9.3
-7.2
2.05
2.3
4.06
4.32
4.35
21.3
Step-by-step explanation:
negatives go 1st. the bigger the number would be positive means its a smaller negative. then you just order the positive numbers least to greatest
No sé nada de esto, solo quiero los puntos, así que no se enoje conmigo por tener que publicar algunas preguntas, traduzca esto y, a cambio, responderé una pregunta realmente seria. entonces byeeeeeeee
The function f(x) = 6x + 8 is transformed to function g through a horizontal stretch by a factor of 5. What is the equation of function g? Replace the values of a and k in the function equation. G(x)=6^ax +k
Answers
Answer:
\(g(x) = 30\cdot x +40\); \(a \approx 1.898\), \(k = 40\).
Step-by-step explanation:
The resultant function is obtained by multiplying \(f(x)\) by a real number \(k\). That is:
\(g(x) = k \cdot f (x)\)
If \(k = 5\) and \(f(x) = 6\cdot x + 8\), then \(g(x)\) is:
\(g(x) = 5\cdot (6\cdot x + 8)\)
\(g(x) = 30\cdot x +40\)
Given that presence of the expression \(g(x) = 6^{a}\cdot x + k\), then:
\(6^{a} = 30\) and \(k = 40\)
The value of a is obtained by applying the definition of logarithms:
\(a = \log_{6}30\)
\(a \approx 1.898\)
Finally, the value of k is found by direct comparison:
\(k = 40\)
Answer: 1/5 and 8
Step-by-step explanation:
you're valuing horn of plenty mining, inc.'s, stock in order to compare its value to its market price. you believe that the company will pay total dividends of $1.45 in 2015 and $1.56 in 2016. you also believe the company's stock price will be $35.80 at the end of 2016. if the appropriate discount rate is 12 percent, what's the value of horn of plenty mining's stock? a. $39.22 b. $38.31 c. $36.87 d. $37.43
Answers
Step 1: Calculate the present value of each dividend payment.
PV(2015) = $1.45 / (1 + 0.12)^1 = $1.29
PV(2016) = $1.56 / (1 + 0.12)^2 = $1.22
Step 2: Calculate the present value of the expected stock price at the end of 2016.
PV(2016 stock price) = $35.80 / (1 + 0.12)^2 = $28.33
Step 3: Add up the present values of the dividend payments and stock price to get the total stock value.
Stock value = PV(2015) + PV(2016) + PV(2016 stock price) = $1.29 + $1.22 + $28.33 = $30.84
Therefore, the value of Horn of Plenty Mining's stock is $30.84, which means that the correct option is e) None of the above.
Last week, Russell bought 4 books and 4 movies for a total of $108.
Today, Russell bought 15 books and 4 movies for a total of $262.
Assuming neither item has changed in price,
what is the cost of a book in dollars?
Answers
Answer:
a lot of money for 4 books and 4 movies 108
take away 4/5 from 6 1/2
Answers
Answer:
3-4/5=2.2
hope it helps
Hi there!
»»————- ★ ————-««
I believe your answer is:
\(5\frac{7}{10}\)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
\(\boxed{\text{Calculating the answer...}}\\\\6\frac{1}{2}-\frac{4}{5} \\-------------\\6\frac{1}{2} = \frac{13}{2} \\\\\frac{13}{2} - \frac{4}{5}\\\\LCM(2,5): 10\\\\\frac{13}{2} =\frac{13*5}{2*5} =\frac{65}{10}\\\\\frac{4}{5}=\frac{4*2}{5*2}=\frac{8}{10}\\\\\frac{65}{10}-\frac{8}{10}\\\\ \frac{57}{10}\\\\\frac{57}{10}\rightarrow\boxed{5\frac{7}{10}}\)
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
$35.79 for a 22 pound turkey written in unit rate
Answers
Unit rate would be price per pound.
Divide total price by total rate:
35.79/22 = 1.6268
Round to the nearest cent:
$1.63 per pound
The attendance at a new weekly exercise class doubled each week until week 4, when it reached its maximum capacity of 24 people
Answers
Answer:
Half Maximum capacity a week 3. And the class started off with 3 people.
Step-by-step explanation:
PLEASE ANSWER NUMBER 2
Answers
What design principle is stressed for experiments or observational studies?
Choose the correct answer below.
A. Using dependent samples with paired data is generally better than using two independent samples.
B. When using paired data, keep the sample very small in order to keep the data manageable.
C. The methods for dependent samples can be used for any matched pairs.
D. Using two independent samples is the best choice for accurate results.
Answers
Answer:
A). Using dependent samples with paired data is generally better than using two independent samples.
Explanation:
Observational studies is the research/study design in which the investigator observes the samples collected from the population in their natural pattern to make valid inferences without any kind of manipulation or interference. While the experimental studies involves a controlled or manipulated variable in order to check its impact over the independent variable and the relation between the two.
As per the question, the design principle that is emphasized for both the studies would be 'employing dependent samples along with the paired data is usually effective than employing two independent samples' as the former concerns one set of elements that makes them 'self-evident'(as the subjects of one sample can be employed to determine the subjects of other). Thus, option A is the correct answer.
A boy has 30 spellings to learn.
12 words included an 5, 16 a T and 18 an E.
10 words had an E and a T, 6 words had an Sand aT and 5 words had an E and an S.
4 words had all three.
Probability that?
A • the first two spellings in the test both included only one of the three letters?
C• the first two spellings in the test both had an E and at least one other letter
Answers
Answer:
A
Step-by-step explanation:
Please help needed!!
Answers
A point= zero-dimensional object designates a particular place on a plane. Moreover, a little dot is used to symbolize it.
What is a geometric figure?A geometric figure is a collection of lines, planes, or points that together form the shapes of various three-dimensional things.
A geometric figure is referred to in geometry using the terms and definitions below:
A point, or zero-dimensional object, designates a particular place on a plane. Moreover, a little dot is used to symbolize it. ⇒Image 4.A line is a one-dimensional shape that stretches in two (2) directions without having an end. (Image 5)Line segments are the discrete portions of a line that connect any two (2) points on the line. (Image 1.)A ray is a half-line that begins at one place and extends in one direction indefinitely (forever) (Image 3).A plane is a two-dimensional surface that never ends( Image 2.).To know more about Geometry visit:
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a number is one more than twice the other number. their product is 36. what are the numbers
Answers
Answer:
Possible solution 1: -4.5 and -8
Solution 2: 4 and 9.
Step-by-step explanation:
Let the two numbers be a and b.
One of them (let it be b) is 1 more than twice the other one. In other words,
b= 1+ 2a.
Their product is 36. Or:
a(b) = 36.
Substitute b:
a(1+2a) = 36
2a^2 + a = 36
2a^2 + a - 36 = 0
This is now a quadratic. We can factor to solve it. Find two numbers that equals 2(-36)=-72 and add to 1. We can use 9 and -8. Thus:
2a^2 - 8a + 9a - 36 = 0
2a(a - 4) +9(a-4) = (2a+9)(a-4) = 0
So, a = -9/2 = -4.5 or a = 4.
Thus, b can equal 1 + 2(-4.5) = -8 or 1 + 2(4) = 9
What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?
Answers
Answer:
The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is \(\mathbf{y=-\frac{5}{4}x+3}\)
Step-by-step explanation:
We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.
The equation will be of form \(y=mx+b\) where m is slope and b is y-intercept.
Finding slope of the line:
Since both the lines are parallel, and we know that parallel lines have same slope.
The slope of given line \(5x+4y=16\) can be found by writing in slope-intercept form \(y=mx+b\)
\(5x+4y=16\\4y=-5x+16\\y=-\frac{5}{4}x+16\)
Comparing with \(y=mx+b\) the slope m is: \(m=-\frac{5}{4}\)
So, the slope of required line is: \(m=-\frac{5}{4}\)
Now, finding y-intercept b
y-intercept can be found using slope \(m=-\frac{5}{4}\) and point (8,-7)
\(y=mx+b\\-7=-\frac{5}{4}(8)+b\\-7=-5(2)+b\\-7=-10+b\\b=-7+10\\b=3\)
So, we get y-intercept: b=3
Now, the equation of required line having slope \(m=-\frac{5}{4}\) and y-intercept b=3 is:
\(y=mx+b\\y=-\frac{5}{4}x+3\)
So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 \(\mathbf{y=-\frac{5}{4}x+3}\)
Please help!!!!!! If the measure of angle 8 is 35 what is the measure of angle 4?
Answers
Answer:
35
Step-by-step explanation:
Comman knowlege. Also there is a fancy name for them because thay are the same way... Corresponding Angles
Answer:
35 degrees
Step-by-step explanation:
It is congruent to 8 and lined up so it is also 35 degrees.
ASAP PLEASE HURRY
What is the value of q − 8 if q = −18?
A. 26
B. -26
C. 10
D. -10
Answers
Answer:
-26
Step-by-step explanation:
Q = -18
-18 - 8
-26
Hope this helps! :)
mobymax help 11 points math
Answers
Answer:
10/15 + 3/15 = 13/15
Step-by-step explanation:
What is the correct equation for this word problem? Jorge had received some crayons for his birthday. He gave 12 crayons to his friend and had 14 left. How many crayons had he received as a gift?
Question 5 options:
x + 14 = 12
x - 12 = 14
14 + x = 12
12 - x = 14
Answers
Answer:
He was given 26 crayons
Step-by-step explanation:
If he gave 12 and had 14 crayons left, then add 14 + 12 to get your answer
Answer:
x-12=14
he got 26 crayons as a gift.
Step-by-step explanation:
you can find how many he got by taking x (amount he was gifted)
subtract the amount he gave away (12)
then he was left with 14 so
12+14=x
since that isnt an option it is x-12=14 if that makes sense