A machine is used to fill plastic bottles with bleach. A sample of 18 bottles had a mean fill volume of 2.007 L and a standard deviation of 0.010 L. The machine is then moved to another location. A sample of 10 bottles filled at the new location had a mean fill volume of 2.001 L and a standard deviation of 0.012 L. It is believed that moving the machine may have changed the mean fill volume, but it is unlikely to have changed the standard deviation. Assume that both samples come from approximately normal populations and have equal variance. The 99% confidence interval for the difference between the mean fill volumes at the two locations is approximately

Required:
Find a 99% confidence interval for the difference between the mean fill volumes at the two locations.

Answers

Answer 1

Answer:

The 99% confidence interval for the difference between the mean fill volumes at the two locations is;

-0.1175665 L < μ₁ - μ₂ < 0.1295665 L

Step-by-step explanation:

The number of bottles in the sample at the first location, n₁ = 18 bottles

The mean fill volume, [tex]\bar{x}_{1}[/tex] = 2.007 L

The standard deviation, σ₁ = 0.010 L

The number of bottles in the sample at the second location, n₂ = 10 bottles

The mean fill volume, [tex]\bar{x}_{2}[/tex] = 2.001 L

The standard deviation, σ₂ = 0.012 L

The nature of the variance of the two samples = Equal variance

The confidence interval of the statistics, C = 99%

The difference between the mean

[tex]\mu_1 - \mu_2 = \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times \sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}}+\dfrac{\sigma _{2}^{2}}{n_{2}}}[/tex]

(1 - C)/2 = (1 - 0.99)/2 = 0.005, the degrees of freedom, f = n₁ - 1 = 10 - 1 = 9

∴ [tex]t_{\alpha /2}[/tex] = 3.25

Therefore, we have;

[tex]\mu_1 - \mu_2 = \left (2.007- 2.001 \right )\pm 3.25 \times \sqrt{\dfrac{0.01^{2}}{18}+\dfrac{0.12^{2}}{10}}[/tex]

Therefore, we have the difference of the two means given as follows;

-0.1175665 L < μ₁ - μ₂ < 0.1295665 L


Related Questions

In a poll of 2000 likely voters, 960 say that the US spends too little on fighting hunger at home. Find a 96% confidence interval for the true proportion of voters who feel this way. a.Find a point estimate for p, the population proportion who thought US spends too little on fighting hunger at home.b.Find a 96% confidence interval for p.

Answers

Answer:

a. 0.48

b. The 96% confidence interval for p is (0.457, 0.503).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

In a poll of 2000 likely voters, 960 say that the US spends too little on fighting hunger at home.

This means that [tex]n = 2000, \pi = \frac{960}{2000} = 0.48[/tex].

This is the answer for question a.

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.056[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 - 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.457[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 + 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.503[/tex]

The 96% confidence interval for p is (0.457, 0.503).

Which is the better buy, Item A, selling at 5 and 2/3 pounds for $9.52 or Item B selling at 1 1/5 pounds for $1.98? Pls help !!

Answers

Item B would be a better buy

How many laps did Benito swim?
Rate: 10 laps in 6 minutes Time: 30 minutes

Answers

Answer:

50 laps

Step-by-step explanation:

10 laps : 6 minutes

multiply both sides by 5

50 laps: 30 minutes

Need help with one more thing. Find the value of y.

Answers

Answer:

12 or 13

Step-by-step explanation:

one of the two from my knowledge

Answer:

y = 11.82

Step-by-step explanation:

use cos:

⇒ cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

⇒ cos 10 = [tex]\frac{12}{y}[/tex]

cos of 10 is 0.9848

⇒ 0.9848 =  [tex]\frac{12}{y}[/tex]

multiply 12 on both sides

⇒ 0.9848 x 12 =  [tex]\frac{12}{y}[/tex] x 12

⇒ 11.82 = y

Pleaseeee help I'll give Brainliest urgent!!!!!!!!!!!!!!!!!

Answers

Answer:

The answer is

'The range of the data for girls is less than the range of the data for boys'

I'm don't know dfhgh fhfghfg hgf hgfh

Ed walsh wanted to purchase a used car. He obtained a 6,700 installment loan at an APR of 6%. He must repay the loan in 2 years. Find the monthly payment, the total amount repaid, and the finance charge.

Answers

Answer:

$519.43

Step-by-step explanation:

bc it is

There are 85 sixth grade students in Mr. Green’s math class. This makes up 34% of the students in 6th grade in the school. What is the total amount of students in 6th grade?

Answers

Answer:

250

Step-by-step explanation:

Take the part (85) and put it over 34% like a fraction.

85  x

34  100

Then do 85 times 100

8500

Then divide it by your percent (34)

8500/34=250

what is the sum of 2/5 and 2/5 in simplest form

Answers

Answer:

The answer is 2/5

Step-by-step explanation:

2/5+2/5=4/5=2/5


Joyce is making sushi rolls. She needs cup of
rice for each sushi roll. How many sushi rolls
can she make if she has 3 caps of rice?
3
You can use objects or draw
e picture to find the solution

Answers

Answer:

She can make 3 sushi rolls.

Step-by-step explanation:

it's not that hard, but ok

So, if Joyce needs one cup for every sushi rolls and she has 3 cups. You just add 3 + 0, getting you 3.

the difference of p and 7 is 30​

Answers

p - 7 = 30

thats you equation

Answer:

p = 37

p- 7=30

add seven to both sides and you get

p=37

Which of the following equations have no solutions? Select all that apply:
A) 14r + 23 = 14r -23
B) -23r - 14 = 14r -23
C) 14r - 23 = 14r -23
D) -14r + 23 = 14r - 23​

Answers

A) Yes: they would cancel each other out
B) No: r = 9/37
C) Yes: they would cancel each other out
D) No: r = 23/9
The answer is
A.) 14r + 23 = 14r - 23

C.) 14r - 23 = 14r - 23

Find p(–4) if p(x) = x ^3 – 3x^ 2 + 7x + 6.

Answers

Answer:

p(-4) = -134

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

p(x) = x³ - 3x² + 7x + 6

p(-4) is x = -4

Step 2: Evaluate

Substitute in x [Function]:                                                                              p(-4) = (-4)³ - 3(-4)² + 7(-4) + 6Evaluate exponents:                                                                                      p(-4) = -64 - 3(16) + 7(-4) + 6Multiply:                                                                                                           p(-4) = -64 - 48 - 28 + 6Subtract:                                                                                                          p(-4) = -140 + 6Add:                                                                                                                 p(-4) = -134

TRUE or FALSE. Write the word True if the statement is true, and False if the statement is false

1.If my father and mother have a gene coding for obesity, it is guaranteed that I will be obese.

2.Many factors other than genetics may determine whether a person is obese.

3.It is possible that I will inherit other genes from my parents that counter the obesity genes.

4.Phenotypes are the observable characteristics of an individual.

5.Mutations determine differences in the human genome.

Answers

Answer:

Step-by-sTrue

tep explanation:

Answer:

1: False

2: True

3: True

4: True

5: False

Step-by-step explanation:

find the 14th term of the geometric sequence 2,4,8

Answers

Answer:

(0,16) I am pretty sure

Step-by-step explanation:

need help please. urgent!!​

Answers

Answer:

12-3y-2x+x+2x = x-3y+12

3x+2y-2x+y+12 = x+3y+12

4y+3y+3x-6y-10-2 = 3x+y-12

x+3y+2x-3x+7+5 = 3y+12        

Step-by-step explanation:

At East High School, there are a total of 1050 students in the freshman and sophomore classes. However, the freshman class has 80 more students than the sophomore class. Which system of equations could be used to determine the number of freshmen (f) and sophomores (s) in the school?
Choose all that apply.

1. f + s = 1050
s + 80 = f

2. f - s = 1050
f + s = 80

3. f + s = 1050
f + 80 = s

4. f - s = 1050
s + 80 = f

5. f + s = 1050 f - 80 = s

Answers

Answer: Numbers 1 and 5.

Step-by-step explanation:

It will take Taylor alone 15 hours to complete the work alone.

What is function?

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that at East High School, there are a total of 1050 students in the freshman and sophomore classes. However, the freshman class has 80 more students than the sophomore class.

We can write the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -

f + s = 1050

f - 80 = s

Therefore, the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -

f + s = 1050

f - 80 = s

To solve more questions on system of equations, visit the link-

brainly.com/question/29014197

#SPJ2

each of four people shake hands once with each of the other three. how many hand shakes will there be

Answers

Answer:

6

Step-by-step explanation:

o o o o

3+2+1 = 6

What is the final cost of an item priced at $5.70 after a 7% sale tax is applied

Answers

Answer:

the total is $6.10 once applied

and the sale tax is $0.40

Step-by-step explanation:

Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a rectangle ​

Answers

Answer:

prove that opposite sides are congruent and parallel

Step-by-step explanation:

i took the testtttttt

The statement which explains is Prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals, the correct option is D.

We are given that;

The quadrilateral ABCD

Now,

A rectangle is a quadrilateral with four right angles, which means that the slopes of consecutive sides are negative inverses of each other.

For example, if the slope of AB is m, then the slope of BC is -1/m.

Also, a rectangle has opposite sides that are equal in length,

which means that the distance between A and B is the same as the distance between C and D, and the distance between B and C is the same as the distance between A and D.

Therefore, by quadrilateral the answer will be prove that opposite sides are congruent and that the slopes of consecutive sides are opposite reciprocals.

To learn more about quadrilateral visit;

https://brainly.com/question/29934440?referrer=searchResults

#SPJ4

Triangle EFG undergoes a dilation centered at the origin. The result is triangle E'F'G'. Which rule describes the dilation?

A) (x, y) → (2x, 2y)
B) (x, y) → (4x, 4y)
C) (x, y) → ( 1 4 x, 1 4 y)
D) (x, y) → (−4x, −4y)

Answers

Thea answer B) (x, y) → (4x, 4y)

Answer:

B

Step-by-step explanation:

i took test

2^2x - 6(2^x) + 5 = 0

Answers

Answer:

can you please write the expression with the mathematical symbols. I can't understand what you mean by (^). do you mean that number is raised to that symbol or are you're trying to multiply. if you don't know how to write exactly how it's given, attach a picture of your question.

Step-by-step explanation:

First one to answer gets BRAINLIEST no cap look at the picture.

Answers

Answer:

63 sq meters

Step-by-step explanation:

[tex]A=\frac{a+b}{2} h\\\\A=\frac{11+7}{2} *7\\\\A=\frac{18}{2} *7\\\\A=9*7\\A=63[/tex]

A=a+b/2 •9
A=11+7/2 •9
A=18/2 •9
A=9•9
A=81 m^2

Pls help extra points and mark brainlist

Answers

Answer:

Rock layers only (I think this is correct from the searches I've made)

Write 6% as a fraction in simplest form.

Answers

Answer:

Answer is 3/50

Step-by-step explanation:

I hope it's helpful!

Will someone please help me solve this problem.​

Answers

Answer:

A

Step-by-step explanation:

The answer is 64 since it can be a multiple of the numbers

17
Write the integers that are closest to the number in the middle to complete the statement.

Answers

I think it’s 15! Hope this helpsssssss

Olivia sold water bottles over four days. Create a graph to determine if
the quantities of bottles and number of days are proportional If the
quantities are proportional, what is the constant of proportionality?

Answers

Answer:

sorry I cannot help

Step-by-step explanation:

I will try after some time to help u....LOL

enjoy

Anna juices 8 quarts of juice in 1 minute. How many gallons does she have in 1 hour? (4 quarts = 1 gallon)

Answers

Answer: 120

Step-by-step explanation: 8 times 60 is 480 then converted to gallons do

480/4

12(-5z - 4)
please help me

Answers

Answer:

-60z - 48

Step-by-step explanation:

Is your expression.

cuanto es 8/9 x 15/16? porfaAa estoy en prueba

Answers

Answer:

=5/6

Step-by-step explanation:

happy to help ya :)

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