A manufacturer reports that the mean lifetime of its lithium batteries is 1100 hours, but there are customer complaints that the battery life is lower. A consumer advocate group selects 25 of these batteries at random and finds the mean lifetime to be 1080 hours with a standard deviation of 80 hours. The sample data are approximately symmetric and unimodal with no outliers. Check conditions, show how the test statistic is calculated. Test using a 10% significance level. State your conclusion in the context of the problem.

Answers

Answer 1

Answer:

The p-value of the test is 0.1117 > 0.1, which means that there is not significant evidence at the 10% significance level that the battery life is lower than 1100 hours.

Step-by-step explanation:

A manufacturer reports that the mean lifetime of its lithium batteries is 1100 hours, but there are customer complaints that the battery life is lower.

At the null hypothesis, we test that the mean lifetime of the battery is of 1100 hours, that is:

[tex]H_0: \mu = 1100[/tex]

At the alternate, we test that is is lower, that is:

[tex]H_a: \mu < 1100[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

1100 is tested at the null hypothesis:

This means that [tex]\mu = 1100[/tex]

A consumer advocate group selects 25 of these batteries at random and finds the mean lifetime to be 1080 hours with a standard deviation of 80 hours.

This means that [tex]n = 25, X = 1080, s = 80[/tex]

Test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{1080 - 1100}{\frac{80}{\sqrt{25}}}[/tex]

[tex]t = -1.25[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean below 1080, which is found using a left-tailed test for t = -1.25, with 25 - 1 = 24 degrees of freedom.

With the help of a calculator, this p-value is of 0.1117

The p-value of the test is 0.1117 > 0.1, which means that there is not significant evidence at the 10% significance level that the battery life is lower than 1100 hours.


Related Questions

Ms. Silvia earns $3 every time she sells a cupcake. If she earns $15, how many cupcakes did she sell?

Answers

Answer:

Okay very easy, The answer is: She sold 5 cupcakes.

Step-by-step explanation:

She sold 5 cupcakes

Because if you add 3 till you get to 15 you get 5

if you triple the number of times elizabeth has cooked dinner for her family and then add for you get the number of times her sister joy has coached the family's thinner of joy has cut the family's dinner 25 times how many times did has elizabeth cook dinner?​

Answers

Answer:

Step-by-step explanation:

She has cooked 75 times

a polygon is shown what is the measure of U

Answers

Answer:

120

Step-by-step explanation:

That's a guess, but it's the most logical one.

m∠1=(3x+21)° and m∠3=(4x+9)° what is the value of x

Answers

Value of [tex]x[/tex] as per considering given pair as vertical  opposite angles is equals to [tex]12[/tex] degrees.

What are vertical opposite angles?

" Vertical opposite angles are defined as when two straight line intersect each other , the two non adjacent angles are vertical opposite angles. Measure of vertical opposite angles are always equal."

According to the question,

Given measure of angles,

[tex]m \angle1 = (3x + 21)\°[/tex]

[tex]m \angle3= (4x + 9)\°[/tex]

Consider both the angles as vertically opposite angles we get,

[tex]m \angle1 =m \angle3 \\\implies(3x + 21)\° = (4x + 9)\°\\\\\implies 4x -3x = (21 - 9))\°\\\\\implies x = 12\°[/tex]

Hence, value of [tex]x[/tex] as per considering given pair as vertical  opposite angles is equals to [tex]12[/tex] degrees.

Learn more about vertical opposite angles here

https://brainly.com/question/18045519

#SPJ2

Tessellations

How do you distinguish between problems requiring area formulas and problems requiring perimeter formulas?

a. area - space inside a figure perimeter - distance around figure
b. area - distance around figure perimeter - space inside a figure
c. area - twice the width plus twice the length perimeter - length times width
d. area - the sum of all sides perimeter - 2 times the diagonal of the figure

Please select the best answer from the best choices provided

Answers

Answer:

A. Area - space inside a figure perimeter - distance around figure

Step-by-step explanation:

I calculated it logically

What is the sum of the first ten terms in a geometric series
with a1=
6 and r = 2?

Answers

Answer:

[tex]S_{10} = 682[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 6; r = 2[/tex]

Required

[tex]S_{10[/tex]

This is calculated as:

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

So, we have:

[tex]S_{10} = \frac{6 * (2^{10} - 1)}{10 - 1}[/tex]

[tex]S_{10} = \frac{6 * (1024- 1)}{9}[/tex]

[tex]S_{10} = \frac{6 * 1023}{9}[/tex]

[tex]S_{10} = 682[/tex]

Plz Help!! I’m stuck on this.

Answers

Answer:

1. (5,7)

2. (8,0)

3. (2,1)

4. (4,22)

5. (-3,78)

6. (2,10)

7. (3,9)

8. (-2,1)

Step-by-step explanation:

NO LINKS. Find the measure of the angle or arc indicated. Part 2

Answers

9514 1404 393

Answer:

  14.  C) 136°

  15.  C) 40°

Step-by-step explanation:

Inscribed angles are half the measure of the arc they intercept. For an inscribed quadrilateral, this means opposite angles are supplementary.

__

14) ∠H +∠W = 180°

  34x +55x +2 = 180

  89x = 178 . . . . . . . . . subtract 2

  x = 2 . . . . . . . . . . . . . divide by 89

  arc VX = 2(34x) = 68(2) = 136 . . . degrees

__

15) The sum of angles in the triangle is 180°.

  ? + 80° + (120°/2) = 180°

  ? = 40° . . . . . . . . . . subtract 140°

Answer:

Solution given:

14.

34x+55x+2=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]

89x=180°-2

x=178/89

x=2°

now

m arc VX=2× <H[ central angle is twice the inscribed angle standing on a same base]

m arc VX=2(34×2)=136°

Option C.

15.

Solution given:

<B=80°

<C=½ arc AB[central angle is twice the inscribed angle standing on a same base]

<C=½×120°=60°

we have

<A+<B+<C=180°[ sum of interior angle of a triangle is 180 ]

<A=180-80°-60°

<A=40°

option C.

Factor 3x2 + 42x + 147 completely.

A) 3(x + 1)(x + 49)
B) (3x + 21)(x + 7)
C) 3(x + 7)2
D) (3x + 7)2

Answers

The correct answer is C

Only answer if you’re sure... will give Brainly thank you :)

Answers

Answer:

Step-by-step explanation:

f(x) = x^2 + 3x - x/2

f(x) = x^2 + 2.5x    

   

3x - 1/2x = 6x/2 - 1/2x = 5x/2 = 2.5x

f(6) = 6^2 + 2.5*6

f(6) = 36 + 15

f(6) = 51

Which pair of expressions is equivalent using the Associative Property of Multiplication?
A. 4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
B. 4(2a ⋅ 5) = 8a ⋅ 20
C. 4(2a ⋅ 5) = (2a ⋅ 5) ⋅ 4
D. 4(2a ⋅ 5) = 4 ⋅ 2a ⋅ 5

Answers

Answer:

4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5

Step-by-step explanation:

Let A, B and C be the required expression, according to Associative property;

(A+B)+C = A+(B+C)

This shows that no matter the sum of values in parenthesis, it does not alter the values at both sides.

From the given expression, the expression that is equivalent using the Associative Property of Multiplication is  4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5

Note that the product of the values in bracket do not affect the final values

4(2a ⋅ 5) = 4(10a) = 40a

(4 ⋅ 2a) ⋅ 5 = 8a ⋅ 5 = 40a

You can see that both expressions gives the same values

Click on three points that are solutions to y = 2x + 1.
A. (0,0)
B. (0, 1)
C. (1,0)
D. (1,3)
E. (2,5)
F. (4,8)

Answers

Answer:

B, D, E

Step-by-step explanation:

what's the answer to the picture below

Answers

9514 1404 393

Answer:

  B.  √900

Step-by-step explanation:

The solutions to the equation are ...

  x = ±√900 = ±3√100 = ±10√9 = ±30

Of the offered choices, the only one that matches any of these is ...

  √900

Match the items in a credit card statement to their descriptions.

the maximum credit available on a credit card

determines the finance charge
payable on credit purchases

the amounts debited to the credit card account

the period for which transactions are
recorded in a credit card statement

1.billing cycle
2.annual percentage rate
3.credit line
4.new purchases

Answers

the maximum credit available on a credit card
1. credit line
determines the finance charge payable on credit purchases
4. new purchases
the amounts devoted to the credit card account
2. annual percentage rate
the period for which transactions are recorded in a credit card statement
1. billing cycle

Answer:

Billing cycle: The period for which transactions are

recorded in a credit card statement

Annual Percentage Rate: Determines the finance charge

payable on credit purchases

Credit Line: The maximum credit available on a credit card

New Purchases: The amounts debited to the credit card account

Step-by-step explanation:

Took the test on Edmentum and got 5/5

The school that Emily goes to is selling tickets to the annual dance competition.

On the first day of ticket sales the school sold 3 senior citizen tickets and 14 child tickets for a total of $145.

The school took in $178 on the second day by selling 6 senior citizen tickets and 14 child tickets.

Find the price of a senior citizen ticket and the price of a child ticket.

Answers

Answer:

price for senior citizen is $11

price for child ticket is $8

The base of a rectangular prism has an area of 6 cm². The height of the
rectangular prism is 5 cm. What is the volume of the prism?

Answers

Answer:

30 cm ^3

Step-by-step explanation:

Volume = Length x Width x Height

L and W =6cm^2

H=5cm

Hope this helps!

Simplify the expression. - 17b + a +235 + 240​

Answers

Answer:

a-17b+475

Step-by-step explanation:

Let's simplify step-by-step.

−17b+a+235+240

Combine Like Terms:

=−17b+a+235+240

=(a)+(−17b)+(235+240)

=a+−17b+475

Answer:

=a−17b+475

-17b+a+235+240 is −17+475

Imagine we paint a 4x4x4 cube blue on every side.how many of the small cubes have 3 blue faces? How many have 2 blue faces? How many have 1 blue face? How many have not been painted at all? And how many faces would be painted in a cube of any size.think visually
PLEASE ANSWER ASAP. WILL MARK BRAINLIEST!

Answers

1. 8 small cubes
2. 8 small cubes
3. 20 small cubes
4. 8 small cubes
I believe that is the correct answer sorry if I’m wrong

WHATS THE ANSWER?? answer ASAP NO FILE AT ALL

Answers

Answer:

B

Step-by-step explanation:

Answer:

The answer would be B!

Kari worked twice as many hours as Chris. She also worked ten less than three times as many hours as Mark. Chris and Mark worked the same number of hours.

Answers

Answer:

Kari = 20 hours

Chris = 10

Mark = 10

Explanation:

K is Kari's hours

C is Chris's hours

Karis = 2 x C = K

Chris = C

Mark = C

3C - 10 = K

Assume C is 10 (since 10 is 1/3 of the hours mentioned)

2 x 10 = 20 so K worked 20 hours

20 is twice as much as 10 (C's hours)

and it's 30 - 10 (10 less than 3 times as many hours as Mark)

find two numbers if there sum is -11 and there difference is 41

Answers

x = 26. y = -15

Step-by-step explanation:

Let x and y be the two numbers

x + y = 11. #1

x - y = 41. #2

Adding the two equations together, we get

2x = 52 ----> x = 26

Using this value on equation #2, we get

26 - y = 41

or y = -15

You are giving a bag of jelly beans. There are 7 red, 8 blue, 4 elbow, and 10 pink. Find the probability of eating 3 red jelly beans in a row

Answers

Okay so the probability of drawing a blue bean is

8 / 29 = .276

29 is the total number of jelly beans

When we have replacement, we do not reduce the number of total jelly beans, so the probably of drawing blue stays the same.

But to find the probability of drawing a blue two times in a row, we must square the probability .

(.276) • (.276) = 0.076

Your answer is 7.6% !

Find an equation for the inverse for each of the following relations.
4. y = x - 5

Answers

Answer:

y = x + 5

Step-by-step explanation:

We need to find the inverse of the given relation . Firstly replace x with y and then solve for y to get the inverse . We have ,

=> y = x - 5

Replacing x and y

=> x = y - 5

=> y = x + 5

Hence the Inverse of the relation is y = x + 5 .

Olivia's team played 8 games of basketball. During those 8 games her team's score was: 70, 67, 79, 66, 64, 80, 64 and 75. Find the mode and range

Round to the nearest TENTH.

Question 3 options:

Answers

Answer:

64 is the mode and

it goes from 64, 64, 66,67, 70, 75, 79, and 80, so the range is 80- 64 which is 16

Step-by-step explanation:

y=-1/4(x-10)^2+28 write in standard form

Answers

Answer:

[tex]y = -\frac{1}{4}x^{2} + 5x + 3[/tex]

What is the volume of the rectangular prism? . choices: (63yd^3) (7yd^3) (22.5yd^3) (189yd^3)​

Answers

Answer: (7yd^3)

Step-by-step explanation:

Width= [tex]3*\frac{1}{3}[/tex]

Length= [tex]7*\frac{1}{3}[/tex]

Height= [tex]9*\frac{1}{3}[/tex]

Width= 1

Length= 2.33333333333...

Height= 3

1*2.33333333333*3= 6.99999999999

6.99999999999 is round up to 7

So that would be (7yd^3)

Answer:

Step-by-step explanation:

I just did the test. Answer is 7yd

What is the sum of the whole number and the improper fraction?
4+7/4 A. 4 3/4 B. 5 3/7 C. 5 3/4 D. 4 3/7

Answers

Answer:

C. 5 3/4

Step-by-step explanation:

You have to write all numerators above the common denominator

4+7/4=16+7/4

Add the numbers together

16+7/4=23/4

Simplify the fraction

23/4=5 3/4

The image
shown at the right contains many triangles.
Describe the different types of triangles found in
the image.

Answers

Answer:

Cna you please put a image, I would like that so much so I can help you?

Step-by-step explanation:

hi there is no picture here to show the image

DOES ANYONE KNOW THE ANSWERS TO THESE PROBLEM, PLZ HELP!

Answers

Answer:

Q.1.

Sum of angles of a triangle = 180°

∠A + ∠B + ∠c = 180

(3x - 9) + (4x + 15) + 90 = 180

3x - 9 + 4x + 15 + 90 = 180

7x + 96 = 180

7x = 84

x = 12

∠A = 3x - 9 = 3(12) - 9 = 36 - 9 = 27°

∠B = 4x + 15 = 4(12) + 15 = 48 + 15 = 63°

∠A = 27°

∠B = 63°

Q.2.

[tex]using \ pythagoras \ theorem \\x^2 = 7^2 + (7\sqrt{3} )^{2} = 49 + 49(3) = 196\\x = \sqrt{196} = 14[/tex]

[tex]sin y = \frac{opposite}{hypotenuse} = \frac{7\sqrt{3} }{14} = \frac{\sqrt{3} }{2} \\\\y = sin^{-1} (\frac{\sqrt{3} }{2} ) = 60[/tex]

x = 14

y = 60°

Solve the simultaneous equations
4x3y=32
4x-y=16

Answers

Step-by-step explanation:

Solve equation [2] for the variable y

[2] y = -4x + 16

// Plug this in for variable y in equation [1]

[1] 4x + 3•(-4x+16) = 32

[1] -8x = -16

// Solve equation [1] for the variable x

[1] 8x = 16

[1] x = 2

// By now we know this much :

x = 2

y = -4x+16

// Use the x value to solve for y

y = -4(2)+16 = 8

Solution :

{x,y} = {2,8}

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