1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergio [31]
3 years ago
15

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 45.0 37.8 33.3 50.5 44.0 42.0 Public Colleges 20.3 22.8 22.0 25.8 28.2 18.5 15.6 25.6 24.1 14.4 28.5 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.
S1 =
S2 =
b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place.
Interpret this value in terms of the annual cost of attending private and public colleges.$
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges.
Mathematics
1 answer:
Masteriza [31]3 years ago
5 0

Answer:

Step-by-step explanation:

a) For private colleges,

Mean = (52.8 + 30.6 + 43.2 + 45.8 + 45.0 + 37.8 + 33.3 + 50.5 + 44.0 + 42.0)/10 = 42.5

x1 = 42.5 × 1000 = 42500

Standard deviation = √(summation(x - mean)²/n

n = 10

Summation(x - mean)² = (52.8 - 42.5)^2 + (30.6 - 42.5)^2 + (43.2 - 42.5)^2 + (45.8 - 42.5)^2 + (45.0 - 52.5)^2 + (37.8 - 42.5)^2 + (33.3 - 42.5)^2 + (50.5 - 42.5)^2 + (44.0 - 42.5)^2 + (42.0 - 52.5)^2 = 598.56

standard deviation = √(598.56/10 = 7.74

s1 = 7.74 × 1000 = 7740

For public colleges,

Mean = (20.3 + 22.8 + 22.0 + 25.8 + 28.2 + 18.5 + 15.6 + 25.6 + 24.1 + 14.4 28.5 + 21.8)/12 = 22.3

x2 = 22.3 × 1000 = 22300

n2 = 12

Summation(x - mean)² = (20.3 - 22.3)^2 + (22.8 - 22.3)^2 + (22 - 22.3)^2 + (25.8 - 22.3)^2 + (28.2 - 22.3)^2 + (18.5 - 22.3)^2 + (15.6 - 22.3)^2 + (25.6 - 22.3)^2 + (24.1 - 22.3)^2 + (14.4 - 22.3)^2 + (28.5 - 22.3)^2 + (21.8 - 22.3)^2 = 225.96

standard deviation = √(225.96/12 = 4.34

s2 = 4.34 × 1000 = 4340

b) The point estimate is the difference between the sample means

Point estimate = 42500 - 22300 = 20200

The best guess for the difference in population mean annual cost of attending private and public colleges is $20200. The range of the value is determined by the margin of error.

c) Confidence interval = point estimate ± margin of error

Margin of error = z√(s²/n1 + s2²/n2)

Where z is the test score for 95% confidence level from the t distribution table. To find the test score, we would first find degree of freedom, df

df = (n1 - 1) + (n2 - 1) = (10 - 1) + (12 - 1) = 20

From the t distribution table,

z = 2.086

Margin of error = 2.086√(7.74²/10 + 4.34²/12) = 4.84

4.84 × 1000 = 4840

Confidence interval = 20200 ± 4840

You might be interested in
Help! Fast! Don't want to fail Please!
Marta_Voda [28]
1. 45
2. idk
3. See attached
4. 190

6 0
2 years ago
What is the height of the Tree?<br> 2 m<br> 3 m<br> 30 m
lisabon 2012 [21]

Answer:

The height of the tree is 3m

8 0
2 years ago
A student solved 6x+4=2(x−8) in four steps as shown:
mr_godi [17]
The first thing you should do is solve the equation yourself.

1) Distribute the 2.  
6x + 4 = 2x – 16

2) Next, you'll want to get the x's on one side. So add -2x to both sides.
6x + 4 + -2x = 2x + -2x - 16
4x + 4 = -16

3) Now subtract 4 from both sides
4x + 4 – 4 = -16 – 4
4x = -12

4) Finally, divide both sides by 4
4x/4 = -12/4
x = –3

To solve this problem all you need to do is look back out you work, and figure out the correct solution. The answer the question is The student made an error in Step 1.

7 0
3 years ago
On Monday Sophie ran 4 5/6 laps of a running track and on Tuesday she ran 5 3/4
MatroZZZ [7]

Answer:

10  7/12

hope this is right

Step-by-step explanation:

4  5/6 = 29/6 as an improper fraction

5  3/4 = 23/4 as an improper fraction

you times the two denominators together = 24

you times 29 by 4 = 116

you times 23 by 6 = 138

you add 116 and 138 = 254

you put this over 24 =  254/24

simplify this = 127/12

you make this a mixed number = 10 7/12

the answer is 10 7/12

3 0
3 years ago
12.93 is what percent of 172.40?
Maurinko [17]

Answer:

<h2>7.5%</h2>

Step-by-step explanation:

METHOD\ 1:\\\\\begin{array}{ccc}172.4&-&100\%\\12.93&-&p\%\end{array}\qquad\text{cross multiply}\\\\172.4p=(12.93)(100)\\\\172.4p=1293\qquad\text{divide both sides by 172.4}\\\\p=7.5\ (\%)

METHOD\ 2:\\\\\dfrac{12.93}{172.4}\cdot100\%=\dfrac{1293}{17240}\cdot100\%=0.075\cdot100\%=7.5\%

6 0
3 years ago
Read 2 more answers
Other questions:
  • A dilation with a scale factor of 15 and centered at the origin is applied to MN¯¯¯¯¯¯¯ with endpoints M(−2, −4) and N(1, 5) . D
    7·2 answers
  • See question above<br> 11.5 km<br> 9.5 km<br> 9 km<br> 9.7 km
    14·1 answer
  • Mr. and Mrs. Rainer took out a $240,000 loan to purchase their home. If the interest rate on the loan is 1.2% compounded bimonth
    11·1 answer
  • Find the sum of 2x+1 and 5x
    8·2 answers
  • A square box is filled with two layers of identical square pieces of chocolate. Kirill had eaten all 20 pieces in the upper laye
    13·2 answers
  • The price of a community pool membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function
    12·1 answer
  • Ut 28, <br> –<br> 46, and 8 in order from least to greatest.
    15·1 answer
  • Using your own words, explain direct and inverse proportionality. (Be sure to use complete sentences.)
    14·2 answers
  • Find the odds:
    5·1 answer
  • Find the missing side length of side c, a and b are both 25
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!