A random survey of enrollment at 35 community colleges across the United States yielded the following figures:

6,416; 1,550; 2,110; 9,351; 21,830; 4,299; 5,945; 5,722; 2,827; 2,046; 5,481; 5,202; 5,855; 2,749; 10,011;
6,356; 27,000; 9,415; 7,683; 3,202; 17,502; 9,200; 7,380; 18,315; 6,557; 13,714; 17,767; 7,491; 2,769;
2,861; 1,264; 7,284; 28,165; 5,081; 11,624.

Assume the underlying population is normal.

a. Which distribution should you use for this problem? Explain your choice.
b. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.

i. State the confidence interval.
ii. Sketch the graph.
Iii. Calculate the error bound.

c. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

Answers

Answer 1

Answer:

(6243.99, 11014.53) ; 2385.27 ; (7998.17, 9260.34) ;

Step-by-step explanation:

Given the data:

6416; 1550; 2110; 9351; 21830; 4299; 5945; 5722; 2827; 2046; 5481; 5202; 5855; 2749; 10011; 6356; 27000; 9415; 7683; 3202; 17502; 9200; 7380; 18315; 6557; 13714; 17767; 7491; 2769; 2861; 1264; 7284; 28165; 5081; 11624

Using calculator :

Sample mean, m= 8629.25714

Sample standard deviation, s = 6943.92362

1.) T test distribution ;

Sample size, n = 35

Confidence interval (C. I) : m ± Zcritical * s/sqrt(n)

n = sample size = 35

Tn-1,0.025 = t34, 0.025 = 2.0322

C.I = 8629.25714 ± 2.0322 * (6943.92362 / sqrt(35))

C.I = 8629.25714 ± 2385.2689

Lower bound = 8629.25714 - 2385.2689 = 6243.98824

Upper bound = 8629.25714 + 2385.2689 = 11014.52604

(6243.99, 11014.53)

Error bound :

E = t34, 0.025 * (s/sqrt(n))

E = 2.0322 * 6943.92362 / sqrt(35)

E = 2.0322 * 1173.7373

E = 2385.27

C.)

If n = 500

C.I = 8629.25714 ± 2.0322 * (6943.92362 / sqrt(500))

C.I = 8629.25714 ± 631.08285

Lower bound = 8629.25714 - 631.08285 = 7998.17429

Upper bound = 8629.25714 + 631.08285 = 9260.33999

(7998.17, 9260.34)

Error bound :

E = t34, 0.025 * (s/sqrt(n))

E = 2.0322 * 6943.92362 / sqrt(500)

E = 2.0322 * 310.54170

E = 631.08

Both the error margin and the confidence interval reduces due to large sample size.


Related Questions

An environmental study was conducted. It reported that houses with more inhabitants do not necessarily produce more or less trash. What can be determined?
A. There is no correlation between number of inhabitants and amount of trash produced.
B. There is a correlation between number of inhabitants and amount of trash produced. However, there is no causation. This is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
C. There is a correlation between number of inhabitants and amount of trash produced. There may or may not be causation. Further studies would have to be done to determine this.

Answers

Answer:

C.

Step-by-step explanation:

There's no problem for now but it still needs to be monitored in case something might happen.

I need help please.

Answers

Answer:

the answer is C. 2

Step-by-step explanation:

0.1÷5%

What breaks 40 into 5 equal pieces?

a) 1/2
b) 2/10
c) 2%
d)20%

Answers

Answer:

20

Step-by-step explanation:

20 percent of 40 is 5

so 20 is d answer

25% of 200. Find the percentage of the number

Answers

Answer:

50

Step-by-step explanation:

0.25 * 200 = 50

25% of 200 is 50

Answer:

50

Step-by-step explanation:

25% of 100 is 25 so add another 100 so u have to add 25

Jordan gave her basil plant 86 milliliters of water yesterday. How many liters of liquid did she give her plants

Answers

Answer: 0.086

Explanation: There are 1,000 milliliter in a liter. Since 86 is below 1,000, your answer won’t be in front of the decimal. For example, if you had 3,000 milliliters, your answer would be 3.0 liters.

The ratio of the measures of the sides of a triangle is 2:8:9. If the perimeter of the triangleis 76 inches, find the length of each side. for geometry

Answers

Answer:

The lenghts of the sides are: 8 inches, 32 inches, 36 inches.

Step-by-step explanation:

Perimeter of a triangle:

The perimeter of a triangle is given by the sum of it's sides dimensions.

The ratio of the measures of the sides of a triangle is 2:8:9.

This means that their measures are:

The first measure is x

The second measure is of: [tex]\frac{8x}{2} = 4x[/tex]

The third measure is of [tex]\frac{9x}{2}[/tex]

So the perimeter will be of:

[tex]x + 4x + \frac{9x}{2} = 76[/tex]

[tex]5x + \frac{9x}{2} = 76[/tex]

[tex]\frac{10x}{2} + \frac{9x}{2} = 76[/tex]

[tex]\frac{19x}{2} = 76[/tex]

[tex]19x = 76*2[/tex]

Simplifying by 19

[tex]x = 4*2 = 8[/tex].

So, dimensions of:

[tex]8, 4*8 = 32, \frac{9*8}{2} = 36[/tex]

The lenghts of the sides are: 8 inches, 32 inches, 36 inches.

A medical supplier sells gauze in large and small rectangular sheets. A large sheet has a length of 9 inches and an area of 45 square inches. A small sheet has a length of 4 inches and a width of 3 inches. Are the sheets similar?

Answers

Answer:

Step-by-step explanation:

Large sheet:

 Length = 9 inches

 Width of large sheet = area ÷ length = 5 inches

 ratio of length to width = 9:5

Small sheet:

 Length = 4 inches

 Width = 3 inches

 ratio of length to width = 4:3

9:5 ≠ 4:3

The sheets are not similar

The large sheet and small sheet are not similar because they have different dimensions.

What is the area of a rectangle ?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

It is given that large sheet has a length of 9 inches and an area of 45 square inches whereas the small sheet has length of 4 inches and a width of 3 inches.

Let's find out the area of small sheet which will be :

A = L × B

A = 4 × 3

A = 12 inches²

Whereas , in case of large sheet the area is 45 inches². So , the area of both sheets are not similar.

Let's check if dimensions are same.

Width of large sheet will be :

A = L × B

45 = 9 × B

or

B = 5 inches

So , dimensions are also not equal.

Therefore , the large sheet and small sheet are not similar because they have different dimensions.

Learn more about area of rectangle here :

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solve for da x in 2x+3=7 :>

Answers

Answer:

x = 2

Step-by-step explanation:

Given

2x+3=7

Solve for x

2x = 7 - 32x = 4x = 4/2x = 2

Answer:

2

Step-by-step explanation:

first answer deleted by moderator... even when it was correct... i did more explaining on that one, but they kindly deleted my answer and didn't even show my full answer after they had deleted it like some other moderators do which i always appreciate.

21+15a distributive property equavilent expression

Answers

36 because if you add 21 + 15 you get 36. How by adding it all together. I hope this helped you bye

A farming council takes a large random survey of US adults in which they ask how many times they ate a
cruciferous vegetable such as broccoli, cauliflower, or cabbage in the last 7 days.
Let the random variable x be the number of days a randomly selected respondent reported eating one of these
vegetables
The probability distribution of X and several choices of histograms are shown below
Which histogram correctly displays the probability distribution of the random variable X, the number of days a
randomly selected respondent reported eating a cruciferous vegetable?
a
Ob
Oc
histogram C
histogram A
histogram B

Answers

Answer:

Histogram A

Step-by-step explanation:

Because I was trying to find the answer but I got it wrong and it told me the answer <3

Awnser All 4 boxes pls

Answers

-_- 1x2 3x4 2 3d 34rs 4543 3456

Drag each tile to the correct box.
From the set {1, 2, 3, 4, 5}, find the lowest value of x that makes each inequality true. Arrange the inequalities in increasing order of the lowest value of x from the set that makes them true.
choices...
5x − 3x > 9
2x − 1 > 0
6x − 14 > 3
x + (x − 1) > 5

Answers

Answer: It took me a while but I have the answer! I got them A L L correct! And I also got a 5/0 (100%) on my Edmentum mastery test. Brainliest??????

Step-by-step explanation: (In order!)

2x - 1 > 0

6x - 14 > 3

x + (x - 1) > 5

5x - 3x > 9

Nick works forty hours per week, thirty-five of those hours are paid at the basic rate of
pay (£10 per hour) and the remaining five hours are paid as over-time (£15 per hour).
What is the ratio of basic pay to over-time pay?​

Answers

Answer:

1:1.5

Step-by-step explanation:

if 10:15 when we divide both sides by 10 w get 1:1.5

Abe had some sweets.
He gave half of his sweets to Ben.
Ben gave one third of his sweets to Charlie.
Charlie gave one quarter of her sweets to Dawn.
Dawn gave one fifth of her sweets to Eddy.
Eddy received 6 sweets.
How many sweets did Abe have?

Answers


Answer - 720

You would do 6 x 5 = 30 to get how many dawn had
Then you’d do 30 x 4 = 120 to get how many Charlie had
Then you’d do 120 x 3 = 360 to get how many Ben had
Then 360 x 2 = 720 to get the original amount

Have a good day :)

A fitness machine weigh 16.8 kg. How many grams does the fitness machine weigh?​

Answers

Answer:

16800

Step-by-step explanation:

since the equaltiuon is 16.8*1000

1 kg = 1000 grams.

16.8 kg x 1000 = 16,800 grams

please help me asap ​

Answers

Answer:

1. X=35 degrees obtuse

2 x=25 degrees right

Step-by-step explanation:

Background info:

The measures of the angels of every triangle is 180 degrees

So x equals 180 minus the other angles combined

1. X=180-(40+105)

X=180-145

X=35 degrees

2.

x=180-(90+65)

x=180-155

x=25 degrees

PLEASE HELP Show your work to find the measure of angle L.

Answers

Answer:

if I am guessing this is trigonometry

First is to look at what sides you have in which you have the legs. This means you can use tangent. how ever you need to use arctangent or

tan^-1 to find the angle.

the way you set this up in your calculator is tan^-1(8.4÷15.2). plus be sure it's on Deg not Rad.

This leaves the answer if 28.9°

I hope this helps.

determine whether the following graph represents a function , ILL MARK BRAINLIST

Answers

Answer:

this is not a function

Step-by-step explanation:

which value is the best estimate for x?
A=24.4
B=27.0
C=63.0
D=65.6​

Answers

I think it’s C. 63.0

In the box, type the number that correctly completes the sentence.
A book cost $8.98. Kaitlyn needs $
to buy three books.

Answers

To buy 3 books Kaitlyn will need $27

A nutritionist would like to estimate the number of times adults exercise each week. To collect information, the nutritionist emails the members of the local fitness center. Which of the following describes the bias that may arise from the results?
A- This is a convenience sample and likely overestimates the frequency of exercise.
B- This is a convenience and likely underestimated the frequency of exercise.
C- This is a voluntary response sample and likely overestimates the frequency of exercise.
D- This is a voluntary response sample and likely underestimates the frequency of exercise.

Answers

Answer:

This is a voluntary response sample and likely overestimates the frequency of exercise.

Step-by-step explanation:

I just took the unit test review.  The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.

The statement describes the bias that may arise from the results is "This is a voluntary response sample and likely overestimates the frequency of exercise".

Given that,

A nutritionist would like to estimate the number of times adults exercise each week.

To collect information, the nutritionist emails the members of the local fitness center.

We have to determine,

Which of the following describes the bias that may arise from the results?

According to the question,

A nutritionist would like to estimate the number of times adults exercise each week.

To collect information, the nutritionist emails the members of the local fitness center.

The people taking the survey took it voluntarily and it overestimates exercise because it was offered to gym members.

Hence, This is a voluntary response sample and likely overestimates the frequency of exercise.

To know more about Reasoning click the link given below.

https://brainly.com/question/24572391

add fractions 17/3+5/2=

Answers

Answer:

answer is below

Step-by-step explanation:

49/6 or 8 1/6

solve for x;

2x+3=11?

Answers

Answer:

2x+3=11

2x=11-3

x=8/2

x=4........

Answer: [tex]x = 4[/tex]

Step-by-step explanation:

Okay, so we start with our equation.

[tex]2x + 3 = 11[/tex].

Then we need to get x alone. To do that we subtract the 3 on the side with the x.

But what we do to one side, we do to the other. So we subtract 3 from the 11 as well

2x + 3 = 11    

      -3    -3

2x = 8

Then we divide by 2 on both sides to get X.

[tex]\frac{2x}{2} =\frac{8}{2}[/tex]

[tex]\frac{2x}{2} = x[/tex]

[tex]\frac{8}{2} = 4[/tex]

[tex]x = 4[/tex].

A florist has 733 flowers how many full bouquet of 16 flowers can make?

Answers

Answer:

45 bouquets

Step-by-step explanation:

733 divided by 16 is 45.8125

Round that and you get 45.

Hope this helps!!!

Answer:

45

Step-by-step explanation:

733/16 = 45.81 = 45 and remainder 13

In this case we must round down since with the 13 flowers in the remainder he cannot make another bouquet.

He can make 45 bouquets.

At the football game, 8 out of every 20 spectators were girls. There were a total of 1560 spectators at the game.
How many of the spectators were girls?
Ο Α. 130
Ο Β. 195
C. 624
D. 736
Ε. 1040

Answers

Answer:624

Step-by-step explanation:

10 ways to divide 96 into equal groups

Answers

Answer:

Step-by-step explanation:

48+48=96

32+32+32=96

24+24+24+24=96

12+12+12+12+12+12+12+12=96

6+6+6+6+6+6+6+6+6+6+6+6+6+6+6+6=96

I'm not going to write out the rest of the numbers. I'll multiply them.

4 x 24=96  (etc. 4+4+4....)

3 x 32=96  (etc. 3+3+3....)

2 x 48=96  (etc. 2+2+2....)

1 x 96=96   (etc. 1+1+1....)

I hope this is what you meant. If you liked, mark me Brainliest please.

The number 96 is divided into equal groups, then the number of 10 ways is shown below.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

48 + 48 = 96

32 + 32 + 32 = 96

24 + 24 + 24 + 24 = 96

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 96

6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 96

And the rest are written in the form of multiplication. Then we have

4 x 24 = 96  (etc. 4 + 4 + 4 ....)

3 x 32 = 96  (etc. 3 + 3 + 3 ....)

2 x 48 = 96  (etc. 2 + 2 + 2 ....)

1 x 96 = 96   (etc. 1 + 1 + 1 ....)

More about the Algebra link is given below.

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Zack and Noah jogged 2/5 of a mile and walked another 1/4 of a mile. How far did they go in all?

Answers

Find a common denominator. The lowest one would come from you multiplying 2/5 by 4 on each side and 1/4 by 5 on each side. You are left with 8/20 and 5/20, added together would be 13/20.

In a survey of the most popular type of coffee sold by a cafe, latte recived 42% of the votes expresso recived 3/25 of the votes and ice belended recived 0.46 of the votes. Order the types of coffee from the most popular to the least popular.

Answers

Expresso (most popular)
Latte (medium popular)
Ice blended (least popular)

Explanation:
42%=0.42 (move the decimal two to the left)
3/25=0.12 (divide)
0.46=0.46 (self explanatory)

The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation of $0.86. If a random sample of 12 batches of granola bars is selected, what is the probability that the mean cost will be more than $7.00?


0.2220

0.2339

0.7653

0.7780

Answers

Answer:

0.7780

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

We have that [tex]\mu = 7.19, \sigma = 0.86[/tex]

Sample of 12:

[tex]n = 12, s = \frac{0.86}{\sqrt{12}} = 0.2483[/tex]

What is the probability that the mean cost will be more than $7.00?

This is 1 subtracted by the pvalue of Z when X = 7. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{7 - 7.19}{0.2483}[/tex]

[tex]Z = -0.765[/tex]

[tex]Z = -0.765[/tex] has a pvalue of 0.222

1 - 0.222 = 0.778

So the answer is 0.7780

There was 1 L of water in the water bottle tom drake 200 mL of water how many liters of water are left?

Answers

Answer:

0.8 liters

Step-by-step explanation:

1l=1000 mlml=1000 ml-200ml=800ml=0.8L

Answer:

shouldn't it be 800 mL

Step-by-step explanation:

cause there are 1000mL in 1 liter

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