The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
52.8 30.6 43.2 45.8 33.3
33.3 50.5 44.0 42.0 37.8
Public Colleges
20.3 22.8 28.2 18.5 15.6 25.6
24.1 14.4 28.5 21.8 22.0 25.8
Required:
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
Answer:
(a)
[tex]\bar x_1 =41.33[/tex] [tex]\sigma_1 = 7.48[/tex]
[tex]\bar x_2 =22.3[/tex] [tex]\sigma_2 = 4.53[/tex]
(b)
[tex]d = 19.03[/tex]
(c)
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 10\\ n_2 = 12[/tex]
And the accompanying data for private (1) and public (2) colleges
Solving (a): The sample mean and sample standard deviations
Private College
Calculating sample mean
This is calculated as:
[tex]\bar x_i = \frac{\sum x_i}{n_i}[/tex]
[tex]\bar x_1 =\frac{52.8+30.6+43.2 +45.8 +33.3+33.3 +50.5 +44.0 +42.0 +37.8}{10}[/tex]
[tex]\bar x_1 =\frac{413.3}{10}[/tex]
[tex]\bar x_1 =41.33[/tex]
Calculating sample standard deviation
This is calculated as:
[tex]\sigma_i = \sqrt\frac{\sum(x_i - \bar x_i)}{n_i-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{(52.8-41.33)^2+(30.6-41.33)^2+.........+(37.8-41.33)^2}{10-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{503.261}{9}[/tex]
[tex]\sigma_1 = \sqrt{55.9178888889[/tex]
[tex]\sigma_1 = 7.4778264816[/tex]
[tex]\sigma_1 = 7.48[/tex] -- approximated
Public College
Calculating sample mean
[tex]\bar x_2 =\frac{20.3 +22.8 +28.2 +18.5 +15.6 +25.6+ 24.1 +14.4 +28.5 +21.8 +22.0 +25.8}{12}[/tex]
[tex]\bar x_2 =\frac{267.6}{12}[/tex]
[tex]\bar x_2 =22.3[/tex]
Calculating sample standard deviation
[tex]\sigma_2 = \sqrt\frac{(20.3 -22.3)^2+(22.8 -22.3)^2+(28.2 -22.3)^2+(18.5 -22.3)^2+(15.6 -22.3)^2+................+(25.8-22.3)^2}{12-1}[/tex][tex]\sigma_2 = \sqrt\frac{225.96}{11}[/tex]
[tex]\sigma_2 = \sqrt{20.5418181818[/tex]
[tex]\sigma_2 = 4.532308262[/tex]
[tex]\sigma_2 = 4.53[/tex] -- approximated
Solving (b): Point estimate of the difference between the two population means
This is calculated as:
[tex]d = \bar x_1 - \bar x_2[/tex]
[tex]d = 41.33 - 22.3[/tex]
[tex]d = 19.03[/tex]
Solving (c): 95% confidence interval
First, calculate the degrees of freedom:
[tex]df = \frac{(\sigma_1^2/n_1 + \sigma_2^2/n_2)^2}{\frac{(\sigma_1^2/n_1)^2}{n_1 - 1} + \frac{(\sigma_2^2/n_2)^2}{n_2 - 1}}[/tex]
[tex]df = \frac{(7.48^2/10 + 4.53^2/12)^2}{\frac{(7.48^2/10)^2}{10 - 1} + \frac{(4.53^2/12)^2}{12 - 1}}[/tex]
[tex]df = \frac{53.3647}{31.3045/9 + 2.9244/11}[/tex]
[tex]df = \frac{53.3647}{3.7441}[/tex]
[tex]df = 14.2530[/tex]
[tex]df = 14[/tex]
Calculate the critical value (t)
At 95% confidence interval and df = 14;
[tex]df = 14[/tex]
The confidence interval is then calculated as:
[tex]CI = (\bar x_1 - \bar x_2) \± \sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}[/tex]
[tex]CI = (41.33 - 22.3) \± \sqrt{7.48^2/10 + 4.53^2/12}[/tex]
[tex]CI = 19.03 \± \sqrt{7.305115[/tex]
[tex]CI = 19.03 \± 2.70[/tex]
Split
[tex]CI = 19.03 - 2.70[/tex] to [tex]19.03 + 2.70[/tex]
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
This implies that:
Private colleges have population mean annual cost of $16.33 to $21.73 more expensive than public colleges
Which expression is the simplest form of 2(4x + y) + 3(x - 6y) + x2?
O A. x2 + 11x-17y
B. x2 + 11x – 4y
C. x2 + 9x- 17y
O D. x2 + 11x-16y
Answer:
x² + 11x-16y
Step-by-step explanation:
The given equation is :
[tex]2(4x + y) + 3(x - 6y) + x^2[/tex]
It can be simplified as follows :
[tex]2(4x + y) + 3(x - 6y) + x^2\\\\=2(4x)+2y+3x-3(6y)+x^2\\\\=8x+2y+3x-18y+x^2\\\\=11x-16y+x^2[/tex]
So, the correct option is (d) i.e. x² + 11x-16y.
hey can someone please help me i don’t understand this? the question says “find the surface area of the rectangular prism.”
Answer:
170 in^2
Step-by-step explanation:
you have to find the area of each surface of the square
1) the square on the right side:
5x5=25 in^2
there are 2 of these on opposite sides
2)the of the rectangle facing us;
6x5=30in^2 (5 because 5 is the height)
there are 4 of these
3)add up all the areas
25+25+30+30+30+30=170in^2
To simply a rational expression I should
Answer:
Factorize, then divide the common factors.
Step-by-step explanation:
A rational expression is one that involves the division of two polynomials. The two polynomial having the same variable in each expression.
To simplify a rational expression, the first thing to do is to factorize each expression. This would ensure that there exist a common factor between the numerator and denominator.
Then you can divide by the common factor.
The remaining expressions in the quotient would have been reduced to their simplest form.
1 and 22 are a linear pair, 2 and 3 are a linear pair, and 2 and 4 are vertical angles Which of the following statements is not true?
a. 1=3
b. 2 = 3
C. m 1 + m 4 = 180
d. m 2 + m 3 = 180
Answer:
<1 = <3
m<1 + m<4 = 180
m 2 + m 3 = 180
Step-by-step explanation:
If <1 and <2 are linear pair, hence <1 + <2 = 180
If <2 and <3 are linear pair, hence <2 + <3 = 180
Since <1, <2 and <3 are linear pair, hence <1 and <3 vertically opposite
<1 and <4 will also be a linear pair since they will lie on the same straight line. Since the sum of angle on a straight line is 180, hence <1 + <4 = 180degrees
The correct options are
<1 = <3
m<1 + m<4 = 180
m 2 + m 3 = 180
A mirror has a parabolic surface defined by the equation y =StartFraction 1 Over 24 EndFraction x2 with the vertex (0, 0) at the center of the mirror. When the width of the mirror is 8 inches, what is the depth, y, of the mirror?
1/36 in.
1/6 in.
2/3 in.
2 2/3 in.
ITS C: 2/3 in.
Answer:
Step-by-step explanation:
Edge 2022
Answer:
c
Step-by-step explanation:
2/3 in
Please help me answer this question
Answer: The answer is "tween".
Step-by-step explanation: One of the first usages of the term "tweens" was in the late 1990s referring to children who are in the liminal space between childhood and adolescence. In other words, these children are in a state of “in between.” The culture of tweens originally emerged as a marketing niche directed at preteen girls.
Is the expression below a perfect square?
Is so then factor:
x^2 - 36
Answer:
(x-6)(x+6)
Step-by-step explanation:
Someone please explain this andwer
Answer: 2756 cubic inches
Step-by-step explanation:
Well, first calculate the rectangular prism: 11 x 11 x 16 = 2304
Then the cylinder: pi x 4(sqrd) x 9 = about 452
then add them together
I hope this helps! :)
What is the length,in meters,of VX?
Answer:
C) [tex]\sqrt{90}[/tex]
Step-by-step explanation:
VY = base and leg
XY = height and leg
VX = hypotenuse (c)
VY:
9 - 6 = 3
Solving for VX(c):
a² + b² = c²
3² + 9² = c²
9 + 81 = c²
c² = 90
c = [tex]\sqrt{90}[/tex]
Answer:The answer would be C 90
Step-by-step explanation:
Help me on this pls!!!
Answer:
X=7
Step-by-step explanation:
Hope this helps , good luck ^^
Four groups of some amount equals 52 in a algebraic equation
Answer:
where's the full question
Step-by-step explanation:
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 95% confident that his estimate is within seven percentage points of the true population percentage? Complete parts (a) through (c) below.
a) Assume that nothing is known about the percentage of adults who have heard of the brand,
n= ____________ (Round up to the nearest integer.)
b) Assume that a recent survey suggests that about 81% of adults have heard of the brand.
n= ____________ (Round up to the nearest integer.) Please show work for this one because they change the percentage a lot, so I may have to work this part out myself. Thank you
c) Given that the required sample size is relatively small, cculd he simply survey the adults at the nearest college?
a. No, a sample of students at the nearest college is a cluster sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.
b. Yes, a sample of students at the nearest college is a simple random sample, so the resuls should be representative of the population of adults.
c. No, a sample of students at the nearest college is a stratified sample, not a simple random sample, so it is very possible that the results would not be representaive of the population of adults.
d. No, a sample of students at the nearest college is a convenience sample, not a simple randmom sample. so it is very possible that the results would not be representative of the population of adults.
Answer:
Part A; n= 196
Part B: n = 120
Part C:
d. No, a sample of students at the nearest college is a convenience sample, not a simple random sample. so it is very possible that the results would not be representative of the population of adults.
Step-by-step explanation:
Part A;
The sample size n can be calculated by using the formula
p^ ± z∝/2* √pq/n
this implies that
e= z∝/2* √pq/n
where e= ║p-p^║= 0.07
p^= 0.5
q^= 0.5
Putting the values
e= z∝/2* √pq/n
0.07= ± 1.96 √0.5*0.5/n
Squaring both sides
0.0049 = 3.8146*0.25/n
n= 196
Part B:
Given p^= 0.81 and q^= 1-p^= 1-0.81= 0.19
e= 0.07
Using the formula
e= z∝/2* √pq/n
Putting the values
0.07= ± 1.96 √0.81*0.19/n
Squaring both sides
0.0049 = 3.8146*0.1539/n
n= 119.809= 120
Part C:
The sample selected is not a random sample because all the adults who have heard about the brand do not have equal chances of being chosen.
It is convenience sample that is it is chosen at ease from a nearby college.
i need help fast, thank you!!!
Answer:
D
Step-by-step explanation:
30 multiplied by 1.34 is 40.2
Name the property that the statement illustrates.
Answer:
Reflexive Property of Equality
what is the volume for this figure please I will list brainliest I really need the answer
Answer:
the answer is 708.75
Step-by-step explanation:
4250cm ........... m?
Answer:42.5
Step-by-step explanation:
4250cm = 42,5m
The answer is: 42,5
Hailey made the following statement: "It is impossible t o build a rectangular prism with a volume of 40 units 3 if one side measures 5 units." Key represents 1 cubic unit Select the two figures below that prove Hailey's statement is false.
Answer:
D
Step-by-step explanation:
Answer: B and C / the second one and the third one
Sorry if you already had to submit or answer this :(
Use the formula d=r*t to solve this problem.
Marisol and Mee Young are taking Spain’s AVE train from Madrid to meet up with Marisol’s mother, who is in Seville, which is 336 miles away. If it took them 1.8 hours, how fast were they traveling?
a.
210ph
c.
605 mph
b.
350mph
d.
186 mph
Answer:
D-186
Step-by-step explanation:
I hate edge
Answer:
D-186
Step-by-step explanation:
Got it right
I really need the answer with explanation
Answer:
A = 22 and B = 35
Step-by-step explanation:
The proportional value of x and y is simply
x times 3 1/2 = y
Samantha makes $8.00 an hour babysitting. With the money Samantha earns babysitting, she plans to buy herself a MP3 player that costs $154.00.
Which inequality represents the number of hours Samantha would have to babysit in order to have enough money to buy the MP3 player?
A youth group takes a bus to the movie theater. The cost of a drink is $2.25, the cost of popcorn is $3.45, and the cost of a ticket is $7.00. Each student gets a ticket, a drink, and popcorn. The bus rental costs $100.
If the total cost of the trip is $252.40, how many people went?
Sandra surveyed 15 of her friends to find the number of badges and stickers they owned.
Based on the distribution of data, which observation is correct?
The mean number of stickers is about 1.3 times the mean number of badges.
The mean number of stickers is about 1.3 times the mean number of badges.
The mean number of stickers is about 0.78 times the mean number of badges.
The mean number of stickers is about 0.78 times the mean number of badges.
The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.
The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.
The median number of badges is greater than the median number of stickers because the tallest column is farther right.
The median number of badges is greater than the median number of stickers because the tallest column is farther right.
Answer:
8h ≥ 154
Step-by-step explanation:
Mark me Brainllest
Are the following rectangles similar? Why or why not????
Answer:
No, the small one has a width-to-length ratio of 2/3, and the larger has a ratio of 3/4.
Step-by-step explanation:
No, the small one has a width-to-length ratio of 2/3, and the larger has a ratio of 3/4.
8/12=2/3
18/24=3/4
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 22.4 pounds and a standard deviation of 5.8 pounds. Step 1 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 73 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answer:
sampling distribution = 22.4
sampling deviation = 0.68
Step-by-step explanation:
Given that :
Mean , μ = 22.4
Standard deviation, σ = 5.8
n = 73
Therefore, the sampling distribution of the mean and the standard deviation is
[tex]$\mu_{\overline x} = 22.4$[/tex]
So, [tex]$\sigma_{\overline x}=\frac{\sigma}{\sqrt n}$[/tex]
[tex]$=\frac{5.8}{\sqrt {73}}$[/tex]
= 0.68
So the sampling distribution of the mean is 22.4
The standard deviation is 0.68
0,4+-0,7x(0,2- -0,6)÷0,2=
The answer would be : -2,4
I need help I will give you brainless
Answer:
what are u trying to find, what they each are?
Step-by-step explanation:
Answer:
circle =4
triangle = 2
square = 3
Step-by-step explanation:
circle= c
triangle = t
square = s
2c+t+s =13
t+s = 5
nultiply the second by -1 and add both
2c +t +s = 13
-t-s = -5
2c= 8
c= 4 CIRCLE = 4
3t +4 = 10
3t = 6
t= 2 TRIANGLE = 2
s+2=5
s=3 SQUARE = 3
Pythagorean Theorem is what this is on
Answer:
Not sure what the question is but the equation would be
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]28^{2} = 20^{2} + b^{2}[/tex]
and to find the missing side
784 = 400 + [tex]b^{2}[/tex]
b= 19.6
The missing side would be 19.6
Answer:
19.6
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
What are the factors of x2 - 12x + 36?
Answer:
(x-6) (x-6) or (x-6)^2
Step-by-step explanation:
1.) Find factors of 36 that add up to 12
2.) 6 which makes this a perfect square
3.) you know to subtract because the middle term is negative and the third term is positive (two negatives make a positive)
Which is the best example of an explicit statement from Thoughts and Sentiments that shows Cugoano's beliefs about slavery?
A. “However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever.”
B. “However, it cannot but be very discouraging to a man of my complexion in such an attempt as this, to meet with the evil aspersions of some men, who say, ‘That an African is not entitled to any competent degree of knowledge, or capable of imbibing any sentiments of probity; and that nature designed him for some inferior link in the chain, fitted only to be a slave.’”
C. “By some of such complexion, as whether black or white it matters not, I was early snatched away from my native country, with about eighteen or twenty more boys and girls, as we were playing in a field.”
D. “But the supporters and favourers of slavery make other things a pretence and an excuse in their own defence; such as, that they find that it was admitted under the Divine institution by Moses, as well as the long continued practice of different nations for ages; and that the Africans are peculiarly marked out by some signal prediction in nature and complexion for that purpose.”
Answer:
A. “However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever.”
Explanation:
Ottobah Cugoano's "Thoughts and Sentiments on the Evil of Slavery" provides a personal take on the issue of slavery and how evil of a practice it is for African Americans. At the same time, he also asserted that slaves had the right to rebel against their masters for the treatment they were put under.
One explicit statement that reveals the author's beliefs about the slavery system is "However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever." Through these lines, Cugoano labels slavery as "brutish barbarity, and an unparallelled injustice ... insidious, cruel and oppressive..."
Thus, the correct answer is option A.
Can someone help me? I am stuck on this question! and tysm for the people who helped me!! <3 have a nice day!
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
must be 14
Step-by-step explanation: