An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

Answers

Answer 1

Answer:

The margin of error is of 623.2016.

The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.

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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.

This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]

A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.

This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]

Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

The mean is:

[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]

The standard deviation is:

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]

Confidence interval:

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 = zs[/tex]

[tex]M = 1.96*317.96 = 623.2016[/tex]

The margin of error is of 623.2016.

The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016

The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984

The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).


Related Questions


On an
Air Indian flight there are
9 boys, 5 Indian Children, 0
9 men, 7 foreign boys 14 Indian, 6 indian male
and 7 foreign female. What is the
number of people on board the plane. ​

Answers

Step by Step explanation:

Answer:

43

Step-by-step explanation:

xulxlydlysktstaj4a4uajtajrajra

The people at the Cloak soft drink company believe that their brand of drink is favored over their competitor's brand, Pempsi, by the majority of people. A quick survey is conducted to test this belief. Forty people are asked whether they prefer Cloak or Pempsi, and 28 people did prefer Cloak. A statistician at Cloak wishes to construct a 95% confidence interval for the proportion of people that prefer Cloak soft drink. Drag the blue marker from above the words 'lower bound' to the lower bound of the confidence interval on the number line provided. Drag the red marker from above the words 'upper bound' to the upper bound of the confidence interval on the number line provided.

Answers

Solution :

[tex]$p = \frac{28}{30}$[/tex]

  = 0.93

Given :

[tex]$a=0.05$[/tex]

[tex]$z(0.025)=$[/tex] [tex]$1.96$[/tex]   (from standard normal table)

So the lower bound is

[tex]$=p+z\times \sqrt{p \times \frac{1-p}{n}}$[/tex]

[tex]$=0.7+0.93\times \sqrt{0.7 \times \frac{1-0.7}{30}}$[/tex]

= 1.63 + 0.083

[tex]$=1.73$[/tex]

Dan wants to buy carpet. To cover his hole living room, except for the tiled floor. The tiled floor is 4 5/6 ft by 2 1/3. Find the area the carpet needs to cover

Answers

Answer:

11.2777778 feet (11 feet 321⁄64 inches)

Step-by-step explanation:

Answer:

11 27/100

Step-by-step explanation:

L (length) times W (width) = A (area)


An employee put $10,000 in a retirement
account that offers 4% interest
compounded annually.
The employee makes no additional deposits or
withdrawals. Which amount is closest to the interest
the employee will have earned at the end of 12 years?
A) $4,520.14

B) $5,200.36
C) $6,010.32
D) $7,340.18
PLS ANSWER ASSP WILL GIVE BRAINLIEST ANSWER

Answers

C. $6010, I plugged the information into a simple compound  interest calculator.

The results of a coin toss are shown.

What is P(heads)?

H T H H H T H T T H H T H T T T H H T H T T H H H H T H T T

A. 8/15. B.7/17. C.1/2. D3/5

Answers

Answer:

A is the answer!

Because that's reduced of 16/30

A.

count and divide from 16/30 to 8/15!

Please help me I'm so bad at math and doing AFDA really doesn't help..
place for the solution with quadratic equation

Answers

Answer:

4, 16, -4, 2, -1

x = 4±√(16-4(2)(-1)/4

Correct expression:

Step-by-step explanation:

Given the expression

2x² - 8x - 7 = -4x - 6

Rewrite in standard form

2x² - 8x + 4x - 7 + 6 = 0

2x² - 4x  - 1 = 0

Get the coefficients

Given the standard form ax^2 + bx + c = 0

ax^2 = 2x^2

a = 2

bx = -4x

b = -4

c = -1

Use the general formula to find the factors

x = -b±√b²-4ac/2a

Substitute the coefficients

x = -(-4)±√(-4)²-4(2)(-1)/2(2)

x = 4±√(16-4(2)(-1)/4

Hence the values are 4, 16, -4, 2, -1

Helpppppppppppppppppppppppppppppppppppp

Answers

try this one method. I hope it will help a little

area of square = a^2
25^2 = 625
area of circle = 3.14(r)^2
3.14(12.5)^2 (radius is half of diameter)
=490.625
divide that by 2
=245.31
subtract 625 by 245.31
=379.69
=379.7 ft^2

I’ll give points + brainalist for the correct answer (:

Answers

Answer:

x=18

Step-by-step explanation:

since they are vertical angle they are the same so since its 2x divide 36/2=18

Answer:

x=18

Step-by-step explanation:

[tex]2x = 36 \\ x = \frac{36}{2} \\ x = 18[/tex]

Calculate the area of the following image:

Answers

The area of the pentagon is 247.75

Can someone help me with this one?

Answers

Answer:

well I can see not see the graph so for this the + whatever is the y intercept which means when the line goes through the y axis and with the X find a point that is at the tip of a square then count up or down and if you count up and over it is positive and down and over it negative if i cann the graph I would love to help you.

. El siguiente cuadro muestra el porcentaje de votación que alcanzaron los
cuatro partidos en las últimas elecciones para alcaldes provinciales, en una
provincia en la que votaron 65 000 electores.
Partido %
Progreso posible 42%
Bienestar para todos 28%
Todos unidos 16%
Camino al éxito 12%
Votos nulos o en blanco 2%
¿Cuántos votos más debió obtener el candidato del partido “Bienestar para
todos” para igualar al candidato del partido “Progreso posible”?
a) 14
b) 9 100
c) 27 300

Answers

Answer:

Can you translate?

Step-by-step explanation:

To english..?

What is the balance for B?
DEPOSITS WITHDRAWALS
BALANCE
$565.00
$50,00
А
DATE DESCRIPTION OF TRANSACTION
7/1
7/5
Babyutting
717
Birthday money
7/12
Cell phone bi
7/15
Car Insurance
$95.00
В
$39.20
С
$45.20
D
Lunch with friends
$15.70
E
7/18
7/19
Babysitting
$60.00
F
O 609.90
O 615.00
O 625.60
Ооооо
O 669.90
670,80
O 710.00
1 point
What is the balance for C?

Answers

Firm 27 neoclassical 832
Sjejrj 5929

Find the distance between -4 and 6 on the number line .

Answers

Answer:

10

Step-by-step explanation:

The formula for finding distance between 2 points on a number-line is absolute value. We need to find the absolute value of -4+6. |-4| + |6| = 10

Absolute Value negates any negatives.

The answer is 11 because if you count going from -4 to 6 you get -4,-3,-2,-1,0,1,2,3,4,5,6

Tina owns a house that is worth
$ 125,000, a car that is worth $4,000
and miscellaneous items worth
$3,200. She also has $5,000 in
student loans and $572 in credit card
debt. How much is Tina's net Worth?

Answers

Answer:

126,628

Step-by-step explanation:

125,000+4,000+3,200-5,000-572

Net worth is your dollar amount in assets minus liabilities, so debts and loans, in total the net worth is $126,628

HELP WILL GIVE BRANLIEST

Answers

The whole perimeter is 12 and since it is being dilated you just need to divide 12 divided by 1/2 and you would get 6 unites

Answer: 6

please help me In exponents we have to write​

Answers

Answer:

1.  -3/13

2. (simplified) 8 / (exponential form) 2^3

3. 1265625/16384

4. 5

Step-by-step explanation:

no need for explanation just try the app Photo math (no space in the photo and math)

A plataform is made of two rectangular prisms

Answers

Answer:

12 cubic meters

Step-by-step explanation:

Large - 4x3x2=24

Small - 2x3x2=12

24-12=12

Can someone seriously help me!!!!!

Answers

Answer:

Step-by-step explanation:

This should help I hope

Need the answer. Pic to describe.

Answers

Answer:

Step-by-step explanation:

I think it’s b not sure could be wrong

graph x + 4= -8(y-2)^2

Answers

Answer:

It should be B!

Step-by-step explanation:

The graph looks small and on the left second quadrant

Answer:

Its b

Step-by-step explanation:

Just got it right on edge

Multi-Step Equations - PracticeCheck your SolutionCheck your SolutionCheck your SolutionCheck your SolutionCheck your Solution123456-3m - 5 = 5m - 136(y + 7) = 2(y - 3)3x + 2(x - 5) = 2510q + 3q + 5 = 2(q - 3)(x + 6) = 1323(x - 9)

Answers

Answer:

i don't get what i should do its all messed up

Step-by-step explanation:

What is 11 3/6 rounded to the nearest

Answers

Answer:

12

Step-by-step explanation:

y=x-3
y+3x=1 solve by substitution

Answers

Answer:

x = 1

Step-by-step explanation:

x - 3 + 3x = 1

4x - 3 = 1

4x = 4

x = 1

Answer:

x=1, y=-2

Step-by-step explanation:

According to the substitution property, if x = y, then x can be substituted for y in any equation, and y can be substituted for x in any equation.

We are already given the values:

y=x-3

y+3x=1

We can substitute y into the equation.

As so-

[tex]x-3+3x=1[/tex]

Combine common terms:

[tex]4x-3=1[/tex]

Now solve for x. To solve for a variable, we must isolate it:

Add 3 to both sides:

[tex]4x=4[/tex]

The last thing, 4 is being multiplied to x, so we must divide it to both sides to isolate the variable.

[tex]x=1[/tex]

Now we can just substitute the x value into the y equation:

[tex]y=x-3\\y=1-3\\y=-2[/tex]

It is always better to check our answers, we can substitute our x and y into the equation:

[tex]-2+3(1)=1\\-2+3=1\\1=1[/tex]

We are right! :)) Hope it helps!

x=1, y=-2

(1,-2)

Plz help me with this two question

Answers

Part A:

3.14 X (4)^2 X 3/3
= 50.26548246
50.2 is the answer your welcome

Can somebody give me the answer to this question please

Answers

Answer:

B

Step-by-step explanation:

Football has the highest number of votes in the chart.

11.1.21 A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the males​ surveyed, responded that they had at least one tattoo. Of the females​ surveyed, responded that they had at least one tattoo. Construct a ​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let represent the proportion of males with tattoos and represent the proportion of females with tattoos. Find the ​% confidence interval for . The lower bound is nothing. The upper bound is nothing. ​(Round to three decimal places as​ needed.)

Answers

Complete question :

The Harris Poll conducted a survey in which they asked, "How many tattoos do you currently have on your body?" Of the 1205 males surveyed, 181 responded that they had at least one tattoo. Of the 1097 females surveyed, 143 responded that they had at least one tattoo. Construct a 95% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Answer:

(−0.0085 ; 0.0481)

Step-by-step explanation:

Given that :

n1 = 1205 ; x1 = 181 ; n2 = 1097 ; x2 = 143 ; α = 95%

Zα/2 = 1.96 ( Z table)

Confidence interval : (p1 - p2) ± E

E =Zα/2 * √[(p1q1/n1) + (p2q2/n2)]

p1 = x1 /n1 =181/1205 = 0.1502

q1 = 1 - p1 = 1 -0.1502 = 0.8498

p2 = x2/n2 = 143/1097 = 0.1304

q2 = 1 - p2 = 1 -0.1304 = 0.8696

E = 1.96 * √(0.0001059 + 0.0001033)

E = 0.0283

p1 - p2 = 0.1502 - 0.1304 = 0.0198

Lower boundary = 0.0198 - 0.0283 = −0.0085

Upper boundary = 0.0198 + 0.0283 = 0.0481

(−0.0085 ; 0.0481)

Which side lengths form a right triangle?

Answers

Answer:

Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex] Pythagoras law:h²=p²+b²

needed to apply

4²+8²=12²

80≠144 not a right angled triangle

again

2²+√5²=3²

9=9/

side are a right angled triangle

again

2²+2²=(√8)²

4+4=8

8=8

side are a right angled triangle

What shape are the faces, other than the base,
of a pyramid?

Answers

Answer:

A triangle

Step-by-step explanation:

Will give brainliest if anyone answers this one
LOCKER NUMBERS What is the probability that a 6-digit locker combination with the digits 3, 5, 7, 3, 5, and 2 is the number 53-27-35?

A.1/90
B.1/180
C.1/720
D.1/360

Answers

The answer to your question would be D

Does the equation below represent a
direct proportion? If yes, identify
the constant of proportionality.
х = 6у
A. No
B. Yes, 36
C. Yes, -6
D. Yes, 1/6

Answers

Step-by-step explanation:

The given equation is :

x = 6y ...(1)

Here,

x and y are variables and 6 is a constant number

It means,

x and y are related directly to each other i.e.

x ∝ y

or

x = ky .....(2)

Comparing equation (1) and (2)

k = 6

Hence, yes they are in direct proportion and the value of constant of proportionality is 6.

Answer:

yes / 1/6

Step-by-step explanation:

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