Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee at local fast food restaurants. Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg. If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result

Answers

Answer 1

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that [tex]\sigma = 2[/tex]

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when [tex]M = 0.5[/tex]. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 1.96\frac{2}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 2*1.96[/tex]

Dividing both sides by 0.5

[tex]\sqrt{n} = 4*1.96[/tex]

[tex](\sqrt{n})^2 = (4*1.96)^2[/tex]

[tex]n = 61.5[/tex]

Rounding up

We would have to take a sample of 62 to achieve this result.


Related Questions

HELPP PLEASEEE MY GRADE DEPENDS ON ITTT!!!!!!!!!
Find the value x.

Answers

Answer:

its ten i think it depends on my work

[tex]\\ \qquad\quad\sf\longmapsto 48^2=64\times x[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 48^2=64x[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x=\dfrac{48^2}{64}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x=\dfrac{2304}{64}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x=36[/tex]

What are the solutions to the system?
A. (0, 5.6) and (0, 13)
B. (0, 13) and (16, 1)
C. (4, 10) and (7, 7.75)
D. (16, 1) and (10,0)

Answers

Answer:

(4, 10) and (7, 7.5) are the solutions to this system.

Step-by-step explanation:

You can see this by observing the two given points where the line and the parabola intercept.  Those are the only two points where that will happen.

What is the volume, in cubic meters, of a rectangular prism with a height of 14 meters, a width of 17 meters, and a length of 13 meters?

Answers

Answer:

why is brainlys tutor system not free anymore I really need help from somebody, i used to use tutors so much but now i have none ro help me

Please HELP!! Need answer ASAP

Answers

Answer:

last option:  answer is 'x'

Step-by-step explanation:

(3x + 1 - 1) / 3  =  3x / 3  = x

BRAINLIEST NEED ANSWERS ASAP PLEASE

Answers

[tex]\frac{3x+2+5(x-6)}{x^{2} -36}=\frac{8x-28}{(x+6)(x-6)}[/tex]

someone please answer without links please, thankyouuu

Answers

13 because I did this one believe

Monica drinks 0.125 liters of milk during breakfast and 0.20 liters of milk after dinner everyday. Find the total amount of milk she drinks in a day, using significant digits.

A. 0.325 L
B. 0.33 L
C. 1 L
D. 3.25 L

Answers

The total number of milk drank in a day since the significant figure is not specified is 0.325 L.

What are significant figures?

Significant figures are a way of approximation of large numbers to the required approximation such as two significant figures, three significant figures, or more, as the case may be.

From the given information:

Monica drinks 0.125 liters of milk during breakfast, and0.20 liters of milk after dinner every day

The total number of milk drank in Liters in a day is:

= (0.125 + 0.20) L

= 0.325 L

Learn more about significant figures here:

https://brainly.com/question/24491627

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Answer:

the correct answer is B. 0.33 L

Explanation:

I just took this quiz and this was the correct answer.

help please thanks plsss

Answers

Answer:

A

area = 256 inches²

side = √256 = 16 inches

B

0.0063 inch = 6.3 × 10^-3

Lines a and b are parallel and lines e and f are parallel. Vertical and parallel lines a and b are intersected by horizontal lines e and f. At the intersection of lines a and e, the top left angle is angle 1 and the top right angle is angle 2. At the intersection of lines b and e, the bottom left angle is angle 3. At the intersection of lines b and f, the uppercase right angle is angle 4 and the bottom left angle is angle 5. If m1 = 89°, what is m5? 1 89 91 179

Answers

Answer:

answer is c

Step-by-step explanation:

angle m5 is 91

angle 1 = 89

angle 5= x

180=89-x

180=89+91

Answer:

c (91)

Step-by-step explanation:

trust me

A room in the shape of an octagon has a perimeter of 72 feet. What is the length of each side of the room? Let s represent the length in feet of each side of the room. Write and solve an equation for s.​

Answers

Answer:

s=9

Step-by-step explanation:

8s=72

Divide 72 and 8

s=9

Step-by-step explanation:

Octagon is regular polygon meaning all sides are epual it is 8sided polygon p=72 = sides =8 each side =72÷8

=9feet

Please answer


On the last page of her spiral
she found a note that tells
her to multiply the number
of
pages she has filled by 17.
The note also tells her to
take her answer to the
school office
to pick up a prize if the
answer is correct. What is
the correct answer?
A 2,432
B 1,240
C 2,346
D 2,436

Answers

Answer:

the correct answer is 2,432

Look at the photo! Please help

Answers

the answer is A

Explanation:

Classify the polyhedron. select all that apply-
•non-convex
•non-regular
•convex
•regular

Answers

convex

non-convex

regular

non-regular

Find the equation of the line which passes through (0, 7) at a gradient of 3.

Answers

Answer:

y = 3x + 7

Step-by-step explanation:

Here, line is passing through the point (0, 7). It's x-coordinate is 0 and y-coordinate is 7

So, y-intercept (b) = 7

Gradient (or slope m) = 3

Equation of line in slope intercept form is given as:

y = mx + b

Plugging m = 3 and b = 7 in the above equation, we find:

y = 3x + 7

This is the required equation of line.

Parallel to y = 2x – 5
going through (-6, 1)?

Answers

Answer:

y=2x+13

Step-by-step explanation:

Gradient of parallel lines are equal and in the equation,y=2x-5, 2 represents the gradient.

Therefore the gradient of the other line will also be 2.

Introduce another point (x,y) and then equate using the gradient as follows:

y-1/x--6=2

y-1/x+6=2

Cross multiplication;

(y-1)=2(x+6)

y-1=2x+12

y=2x+12+1

y=2x+13

where is the whole number in 34.50​

Answers

Answer:

34

Step-by-step explanation:

Can someone please help me I will mark u brilliant

Answers

Answer:

1 cubic inch

Step-by-step explanation:

For rectangular prism:

[tex]l = 4 \times \frac{1}{2} = 2 \: in \\ \\ w= \frac{1}{2} \: in \\ \\ h = 2 \times \frac{1}{2} = 1 \: in \\ \\ volume \: of \: prism = lbh \\ = 2 \times \frac{1}{2} \times 1 \\ = 1 \: {in}^{3} [/tex]

Answer: The volume is 1 cubic inch.

Step-by-step explanation:

Volume of 1 cube

V= l*w*h

V= 1/2*1/2*1/2

V= 1/8 or 0.125

Volume of Prism

8*1/8= 1

i need help fast, thank you!!!

Answers

Answer:

D

Step-by-step explanation:

30 multiplied by 1.34 is 40.2

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

GFD and jik...a pair of angles on the outer side

Answer:

<HIK and <GFD

<GFD and <JIK

Step-by-step explanation:

Exterior angles are outside angles.

Hope this helps! :)

Mr. Dorsey and his family are going on a road trip for their family vacation. It will take them 300 total miles. After the first 3 days, they have driven 180 miles. What percent of the driving distance is left after the first 3 days?
Step 1 - How many miles do they have left to drive? ______________

Step 2 - Find the percent this is equal to.

____________ = ______________
100

giving brainly out

Answers

300-180=120 so there is 120 miles left
The percent of the journey is 60% so 40% left
Hoped this helped

The box fill weight of Frosted Flakes breakfast cereal follows a normal distribution with a mean of 9.75 ounces and a standard deviation of 0.27 ounces. A sample of 25 boxes filled this morning showed a mean of 9.85 ounces. At the 0.05 significance level, can we conclude that the mean weight is more than 9.75 ounces per box

Answers

Answer:

Since the calculated value of z= 0.0185 does not lie in the critical region we conclude that  the mean weight is less and equal  to 9.75 ounces per box and accept the null hypothesis.

Step-by-step explanation:

Let the null and alternate hypothesis be

H0:  u ≤ 9.75   against the claim Ha: u > 9.75

Here

Population mean= u= 9.75

Standard deviation= 0.27 ounces

Sample mean= x`= 9.85

Significance level [tex]\alpha[/tex]= 0.05

Using z- test

z= x`-u/s/√n

z= 9.85-9.75/0.27/√25

z= 0.1/5.4

z= 0.0185

The critical region for 1 tailed test at 0.05= z > ±1.645

Since the calculated value of z= 0.0185 does not lie in the critical region we conclude that  the mean weight is less and equal  to 9.75 ounces per box and accept the null hypothesis.

Answer these two questions ASAP please, help is appreciated.

Answers

Answer:

B and A

Step-by-step explanation:

Mark the person above me brainliest
(A question needs two answers so the asker can have the brainliest option)
Best of luck

If D = {1,3,5}, E={3,4,5}, F={1,5,10}

Find

a) ∪

b) ∩

c) ( ∩ )

d) ( ∪ ) ∩

e) ( ∩ )

Answers

Step-by-step explanation:

a)U={1,3,4,5}

b)={1,3,5}

Which Expressions Represent Area?

Answers

Answer:

Step-by-step explanation:

Anna has n number of nickels. She has less than 45 cents. Which inequality could be used to the find the value of n?
A 0.05n < 0.45
B 0.05n > 0.45
C 0.05n < 0.45
D 0.05n > 0.45

Answers

Answer:

The correct answer is A or C 0.05n < 0.45

Step-by-step explanation:

Nickels cost $0.05 and n is the number of nickels, so you multiply the two to get 0.05n. Since this value is less than $0.45, we put a less than sign.

Carla knows that, in order to use adjectives and adverbs more effectively, she needs to understand comparison. Which concepts below can help Carla expand her knowledge?

Each degree of comparison has its own suffix
The positive degree of comparison simply modifies the word and has no suffix
The comparative degree compares two things and uses the suffix –est
The superlative degree compares three things and uses the suffix -est

Answers

Answer:

Each degree of comparison has its own suffix..

Both the adjectives and adverbs are used to make comparisons. The comparatives and superlatives are also used in writing to hedge or to boost the language. Each degree of comparison has its own suffix. The correct option is A.

What is comparative degrees?

The comparative form is used to compare two people, ideas or things. The superlative form with the word 'the' is used to compare three or more. The comparative adjectives are used to compare differences between the two objects they modify (larger, smaller, faster, higher).

The comparative form is used in the sentence where two nouns are compared. The comparative adjectives compare one person or the thing with another and enable us to say whether a person or thing has more or less of a particular quality.

One example of comparative adjective is that Josh is taller than his sister.

Thus the correct option is A.

To know more about comparative degrees, visit;

https://brainly.com/question/1301343

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Which is a function?
O {(-3,5), (1,4), (3,7), (1,7), (4,9)}
O {(7.9), (13,-2), (8,4), (7,0), (4,12)}
O {(2,1), (-1,7), (6,-2), (10,3), (-6,0)}
O {(-2,4), (7,4), (-6,8), (-2,8), (1,1)

Answers

50000000000000000000000000000000000000000000

Answer:

{(7.9), (13,-2), (8,4), (7,0), (4,12)} is a function

Step-by-step explanation:

Eddie wanted to know more about how the cost of fertilizer for his lawn-care business was changing. The cost of a bag of fertilizer just increased from $10 to $15. What is the percent increase of the price?

Answers

The precent increase 1/3rd

A submarine was twenty feet below the surface of the water and descended an additional thirty-two and a half feet. Eventually the submarine ascended forty feet toward the surface of the water. What is the location of the submarine in the water?​

Answers

Answer:

-12 1/2 feet (12 1/2 feet below the surface).

Step-by-step explanation:

I hope this helps! Have a great rest of your day!

A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, there were 1140 downloads of the song, for a total download size of 4522 MB. How many downloads of the standard version were there?

Answers

Answer:

the number of downloads of the standard version is 260

Step-by-step explanation:

Let us assume the downloads of the standard version be x

And, the download of the high-quality version be y

Now as per the question

2.5x + 4.4y = 4522 .........(1)

x + y = 1140

y = 1140 - x .......................(2)

Now put the value of equation 2 in the equation 1

So,

2.5x + 4.4 (1140 - x) = 4522

2.5x + 5016 - 4.4x = 4522

-1.9x = -494

x = 260

Hence, the number of downloads of the standard version is 260

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