A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares to see whether H0: μ = 8 vs. Ha: μ ≠ 8 where μ is the true average weight of the chocolate squares. They calculate the sample mean of the 30 squares to be 8.3 g. Suppose the population standard deviation is 0.87 g and the true weight is 8.5 g. At the 5% level of significance, calculate the power for the test. For full credit, include all steps as described in class.

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that the power of the test is of 0.9992 = 99.92%.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

It 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, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

The mean is [tex]\mu = 8.5[/tex].The standard deviation is [tex]\sigma = 0.87[/tex].A sample of 30 is taken, hence [tex]n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588[/tex].

The power of the test is given by the probability of a sample mean above 8, which is 1 subtracted by the p-value of Z when X = 8, so:

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

By the Central Limit Theorem:

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

[tex]Z = \frac{8 - 8.5}{0.1588}[/tex]

[tex]Z = -3.15[/tex]

[tex]Z = -3.15[/tex] has a p-value of 0.0008.

1 - 0.0008 = 0.9992.

The power of the test is of 0.9992 = 99.92%.

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Related Questions

What is the y-intercept for the equation y=-4(x – 3)2 +1?

Answers

Answer:

(0,25)

Step-by-step explanation:

Answer:

I believe the y intercept is (0,25)

Angelo’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?

Answers

Answer:

the answer is 5 targets

Refer to the following information on full-term births in the United States over a given period of time.Type of Birth Number of BirthsSingle birth 47,200,000Twins 600,000Triplets 3000Quadruplets 200Use this information to estimate the probabilities of the following events.(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures.)

Answers

Answer:

Refer to the following information on full-term births in the United States over a given period of time.

Type of Birth Number of Births

Single birth 47,200,000

Twins 600,000

Triplets 3000

Quadruplets 200

Use this information to estimate the probabilities of the following events.

(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)

(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)

(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures

The radii of two similar cones are 1 and 2.5. What is the ratio of their volumes?

Answers

Answer:

Assuming the cones are the same height, then

V1 = pi * r^2 * h/3 = 3.14159*1^2*h/3

V2 = 3.14159*2.5^2*h/3 = 3.14159*6.25*h/3

V1/V2=(3.14159*h/3)/(3.14159*6.25)*h/3

V1/V2 = 1/6.25 = .16

V2/V1=(3.14159*6.25)*h/3/(3.14159*h/3)

V2/V1=6.25/1 = 6.25

In the expression 12r what values of r makes the expression equal a number less than 12

Answers

answer:

any value below 1

r<1

examples:

12×0=1

12×0.99= 0.0825

12×-12=-144 (which is less than 12)

etc.

10 yd
10 yd

Find the area of each?

Answers

Answer:

20 yards

Step-by-step explanation:

i got 100 0n the quiz

The least common denominator for 3/9 and 3/6

Answers

Answer:

The least common denominator is 18:)

2x+3≤x−5 solve for x

Answers

Answer:

x≤−8

Step-by-step explanation:

2x+3≤x−5

Step 1: Subtract x from both sides.

2x+3−x≤x−5−x

x+3≤−5

Step 2: Subtract 3 from both sides.

x+3−3≤−5−3

Answer is

x≤−8

If the salinity of ocean water at the entrance to an estuary is 35 and 63 percent of the volume of water in the estuary is ocean water, what is the average salinity of the estuary

Answers

The correct answer for the average salinity of the estuary would be 22.235.

Given in the question,

Salinity of ocean water at the entrance to the estuary:  35.

Volume of ocean water in the estuary:  63% (or 0.63).

Volume of freshwater in the estuary:  37% (or 0.37).

Consider, salinity of freshwater as 0.5.

To calculate the average salinity of the estuary, the  formula know is:

Average Salinity = (Salinity of Ocean Water * Volume of Ocean Water + Salinity of Freshwater * Volume of Freshwater) / Total Volume of Estuary

[tex]= \dfrac{35*0.63 + 0.5 * 0.37}{1}\\\\= 22.05 + 0.185\\\\= 22.235[/tex]

Therefore, Average salinity of the estuary would be approximately 22.235.

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A researcher collected data from car shoppers about their favorite car color. He asked 250 people about their favorite vehicle color. How many more people said their favorite color is white compared to those who said black. Your answer should be written as a number not a percentage. And then the percents for the circle graph are 20% red 24% white 32% blue 18% black 4% silver and 2% other

Answers

Answer:

35 more preferred white

Step-by-step explanation:

Black 18% * 250 = 18/100 * 250 = 45

White 32%*250 = 32/100 * 250 = 80

The  difference is 80 - 45 = 35

HELPPP PLEASE!!!!

Write an equation for the nth term of the
arithmetic sequence below.
-12, -3, 6, ...
A. f(n) = -9n - 21
B. f(n) = 9n - 21
C. f(n) = 9n + 21
D. f(n) = -9n + 21
Activate

Answers

Answer: B.f(n)9n-12

Step-by-step explanation:

What is the solution to the system of equations?


(4, 7)
(7, 4)
(12, 5)
(5, 12)

Answers

Question ↷

What is the solution to the system of equations?

3x+2y = 39

5x-y = 13

Answer ↷

(5,12)

Solution ↷

Given that,

3x + 2y = 39......(1)

5x - y = 13.......(2)

multiplying equation 1 by 5 & 2nd by 3 ,we get,

15x + 10y = 195.......(3)

15x - 3y = 39........(4)

Subtracting equation 4th by equation 3rd,

we get,

15x + 10y = 195

-15x - 3y = 39

_____________

ㅤ ㅤ13y = 156

ㅤㅤㅤ y = 12

_____________

so , y = 12 & x = 5

⤿5x-12 = 13⤿5x = 25⤿x = 5

_____________

hence, option 4th ⇢ (5,12) is correct ✓

3x+2y=39--(1)5x-y=13--(2)

Graph Attached

Solution is (5,12)

Option D

solve for x ~
[tex]\bold{2(x + 1) - 4x = 3x + 5} [/tex]

spammers stay away .-.
thankyou ~​

Answers

Answer:

x = -0.6

solving steps:

[tex]\sf \rightarrow 2\left(x+1\right)-4x=3x+5[/tex]

remove the parenthesis

[tex]\sf \rightarrow 2x+2\right)-4x=3x+5[/tex]

group the variables

[tex]\sf \rightarrow 2x-4x-3x\right)=5-2[/tex]

simplify

[tex]\sf \rightarrow -5x\right)=3[/tex]

change sides

[tex]\sf \rightarrow x\right)=\dfrac{3}{-5}[/tex]

answer in fraction

[tex]\sf \rightarrow x\right)=-\dfrac{3}{5}[/tex]

answer in decimals

[tex]\sf \rightarrow x\right)=-0.6[/tex]

Answer:

[tex]x=-0.6[/tex]

Step-by-step explanation:

[tex]2\left(x+1\right)-4x=3x+5\quad :\quad x=-\frac{3}{5}\quad \left(\mathrm{Decimal}:\quad x=-0.6\right)[/tex]

[tex]2\left(x+1\right)-4x=3x+5[/tex]

[tex]2(x+1)-4:-2x+2[/tex]

[tex]-2x+2=3x+5[/tex]

[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}[/tex]

[tex]-2x+2-2=3x+5-2[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-2x=3x+3[/tex]

[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]

[tex]-2x-3x=3x+3-3x[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-5x=3[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-5[/tex]

[tex]\frac{-5x}{-5}=\frac{3}{-5}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=-\frac{3}{5}[/tex]

~Learn with Lenvy~

This table shows the ratio of daisies to roses.
Complete the statement about the equivalent ratios in
this table.
Daisies
Roses
To find the values in each row,
the values
in the previous row by
256
192
64
48
16
12

Answers

Answer:

Its divide and 4

Step-by-step explanation:

To find the values in each row divide the values in previous row by 4.

What is the Ratio?

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Clearly, from observation,
Each column represent geometric progression with common ratio r = 1/4. So when moving downward, the element in the rows decreases as multiple of 1/4.
Here,
R(1, 1) = 256
R (2 ,1) = 64
R(2,1)/R(1,1)=1/4

Thus, To find the values in each row divide the values in previous row by 4.

Learn more about Ratio here:
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7500 in account paying 1.5 compound interest, how much after 8 years

Answers

Answer:

The amount of money after 8 years is $8448.69

Step-by-step explanation:

The rule of the compound interest is  

[tex]A=p(1+r)^{t}[/tex] , where

A is the new valueP is the original valuer is the rate in decimalt is the time in years

∵ There is $7500 in an account

P = 7500  

∵ The account paying 1.5% compound interest

r = 1.5% = 1.5/100 = 0.015  

∵ The money will invest for 8 years

t = 8

→ Substitute all of these values in the rule above to find A  

∵  [tex]A=7500(1+0.015)^{8}[/tex]

→ Use your calculator to find the answer  

A = 8448.69

The amount of money after 8 years is $8448.69

PLEASE HELP WILL GIVE BRAINLIEST!!!!

Answers

Answer:

  C E A F B D

Step-by-step explanation:

A function is translated to the right by h units when x is replaced by (x-h) in the function. So, the larger h is, the farther right the vertex of the quadratic is.

The vertices will be arranged left to right by the ordering ...

  [tex]\boxed{y=f(x+3)}\rightarrow\boxed{y=f(x+2)}\rightarrow\boxed{y=f(x)}\rightarrow\boxed{y=f\left(x-\dfrac{1}{2}\right)}\\\\\rightarrow\boxed{y=f(x-4)}\rightarrow\boxed{y=f(x-7)}[/tex]

Mill river middle school has 320 families with students at the school. For the open house, 240 families were present. What percentage of families came to open house?

Answers

Answer:

75%

Step-by-step explanation:

in order to find the percentage of something like this, all you need to do is divide the part by the whole, thus 240/320 to make 75%

240/320 x 100 = 75%

75% of families came to the open house.

What’s the value of x?

Answers

Answer:

x=15°

Step-by-step explanation:

165°+x=180°(sum of the adjacent angles on a straight line is 180)

x=180-165

x=15°

52. What are the given facts?plssss?help this is​

Answers

Offff ???? You didn’t attach anything

Identify whether each variable is categorical or continuous.

Hand length (cm) ?

Kneeling height (cm) ?

Hours studied for exam ?

Exam score?

Perfect attendance (100=perfect; 0 = not perfect)?

Answers

Answer:

u33u3373737

Step-by-step explanation:

hheeheheheheheheheheheehehehehebeheheheheheheheheehehe

electrician cuts a 21 ft piece of wire into two pieces. One piece is 4 ft longer than the other. How long are the​ pieces?

Answers

21=a+(a+4)

one piece is 8.5 ft

the other is 12.5 ft

Ms. James bought 3 world maps for her classroom. The total cost of the 3 maps was $73.77. The clerk told Ms. James that each map cost $2.45. Do you agree with the clerks calculations? Explain your reasoning.


please help ASAP please will give branlyist if i can figure it out

Answers

Answer:

The clerk is wrong because the total cost per map is $24.59

Step-by-step explanation:

since you know that you spent $73.77 for 3 maps you can set up the equation 73.77 = 3X (where x = cost per map)

once you divide 73.77 by 3 you get 24.59 and that equals the price per map

if it was like the clerk said and each map was 2.45 then the total cost shoud have been 7.35.

the midpoint of (1,4) and (-7,10)

Answers

Answer:

i’m pretty sure the answer is y=3/4x-13/4

Step-by-step explanation:

Choose the expression that is equal to 28.3

Answers

There are no other expressions intered. Please write them too.

Answer:

It CAN be 28.30

D=1/3fk, solve for f

Answers

Answer:

f=3d/k

Step-by-step explanation:

find the value of x ?

Answers

Answer:

Step-by-step explanation:

∠E = ∠G

∠D= ∠F because it’s a parallelogram ==> D=F=2x+12 and E=G=5x

5x+2x+12=180

7x=168

X=24

Solution 2:

2*5x+2*(2x+12)=360

10x+4x+24=360

14x=360-24=336

X=336/14

X=24

Answer:

[tex]{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{☺☺Hope\ it\ helps\ you}}}}}}}}}}}}}[/tex]

A/Q

5x+2x+12=180(Sum of adjacent angles is 180)

=>7x+12=180

=>7x=180-12

=>x=168/7

Hence,x=24....

What is the property name of 3 (6 + 2 ) = ( 3 x 6 ) + ( 3 x 2) ?

Answers

Answer:

The distributive property

Step-by-step explanation:

It says

[tex]a(b+c)=a(b)+a(c)[/tex]

I hope you understand the generalization of the property.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each circle equation to its corresponding center and radius.
center = (3,-5)
radius = 2 units
center = (-3,-5)
radius = 4 units
center = (3,5)
radius = 2 units
center = (-3,5)
radius = 2 units
center = (3,-5)
radius = 4 units
center = (3,5)
radius = 4 units
(x + 3)2 + (1 + 5)2
= 16
(x + 3)2 + (1 – 5)2 = 4
+
=
(x – 3)2 + (x – 5)2
= 4
|(1 – 3)2 + (1 + 5)2 = 16
-
=

Answers

By using the general equation for a circle, we will see that the correct options are:

1) This is a circle centered at (-3, - 5) with a radius of 4 units.2) The center is (-3, 5) and the radius is 2 units.3) The center is (3, 5) and the radius is 2 units.4) This is a circle centered at (3, - 5) with a radius of 4 units.

How to write a circle equation?

For a circle of radius R and center (a, b), the equation is given by:

(x - a)^2 + (y - b)^2 = R^2

With that in mind, if we look at the first equation:

(x + 3)^2 + (y + 5)^2 = 16 = 4^2

This is a circle centered at (-3, - 5) with a radius of 4 units.

For the second equation:

(x + 3)^2 + (y - 5)^2 = 4 = 2^2

The center is (-3, 5) and the radius is 2 units.

The third equation is:

(x - 3)^2 + (y - 5)^2 = 4 = 2^2

The center is (3, 5) and the radius is 2 units.

The fourth equation is:

(x - 3)^2 + (y + 5)^2 = 16 = 4^2

This is a circle centered at (3, - 5) with a radius of 4 units.

If you want to learn more about circles, you can read:

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I love my chocolate company makes dark chocolate and light chocolate

Answers

Answer:

this is great to hear I personally like light

$55 for 20 people............

Answers

Answer:

total amount of money: $1100

Step-by-step explanation:

multiply the number of people by the money for each of them

so $55 x 20 = $1100

Answer:

55 divied by 20..witch mean 50 divied between 20 ppl witch is

11/4 and as a decimal 2.75 hope this helped

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