Space shuttle Challengerexploded because of O-ring failure shortly after it was launched. O-ring damage and temperature at time of launch for the 23 space shuttle flights that preceded the Challenger. The data is reproduced below.
Flights with O-ring damage 43 57 58 63 70 70 75
Flights with no O-ring damage 66 67 67 67 68 69 70 70 72 73 75 76 76 78 79 81
Is the mean launch temperature for flights with O-ring damage significantly less than for flights with no O-ring damage? Use 5% level of significance.

Answers

Answer 1

Solution :

The null and the alternate hypothesis can be stated as :

Null hypothesis

[tex]$H_0:\mu_1 \geq \mu_2$[/tex]

Alternate hypothesis

[tex]$H_a:\mu_1 \leq \mu_2$[/tex]

We known;

[tex]$\overline x_1=\frac{\sum_{i=1}^n X_i}{n_1}$[/tex]

   [tex]$=\frac{43+....+75}{7}$[/tex]

   = 62.286

[tex]$\overline x_2=\frac{\sum_{i=1}^n X_i}{n_2}$[/tex]

   [tex]$=\frac{66+....+81}{16}$[/tex]

   = 72.125

[tex]$s_1^2=\frac{\sum_{i=1}^n(X_i- \overline X_1)^2}{n_1-1}$[/tex]

    [tex]$=\frac{(43-65.5)^2+....+(75-65.5)^2}{7-1}$[/tex]

   = 116.571

[tex]$s_2^2=\frac{\sum_{i=1}^n(X_i- \overline X_2)^2}{n_2-1}$[/tex]

    [tex]$=\frac{(66-72.13)^2+....+(81-72.13)^2}{16-1}$[/tex]

   = 23.45

Therefore, calculating the test statics :

[tex]$t=\frac{\overline x_1 - \overline x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$[/tex]

[tex]$t=\frac{62.29-72.125}{\sqrt{\frac{116.571}{7}+\frac{23.45}{16}}}$[/tex]

[tex]$t=\frac{-9.839}{4.2566}$[/tex]

 = -2.312

Now calculating the P-value for the test as follows :

P=T.DIST(t, df)

[tex]$df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s^2_2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s^2_X}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s^2_Y}{n_2}\right)^2}$[/tex]

[tex]$df=\frac{\left(\frac{116.571}{7}+\frac{23.45}{16}\right)^2}{\frac{1}{7-1}\left(\frac{116.571}{7}\right)^2+\frac{1}{16-1}\left(\frac{23.45}{16}\right)^2}$[/tex]

    [tex]$=\frac{328.2868}{46.36395}$[/tex]

   [tex]$\approx 7$[/tex]

P=T.DIST(t, df)

 =T.DIST(-2.31, 7)

 = 0.0270

Thus, the [tex]$\text{P-value}$[/tex] of the test is P = 0.0270 is [tex]$\text{less}$[/tex] than the level of significance [tex]$\alpha= 0.05$[/tex]. Hence the researcher can reject the null hypothesis.

Conclusion: The mean launch temperature for the flights with O ring damages less than that for the flights with no O rings.


Related Questions

Can you help me answer this question???????

Answers

3^10/ 3^-2
3^12
good luckkkk

Answer:

3^12

Step-by-step explanation:

Which student evaluated the power correctly?
Aida’s Work
5 Superscript 4 = 5 times 5 times 5 times 5 = 625
Hector’s Work
5 Superscript 4 = 5 times 4 = 20
Camila’s Work
5 Superscript 4 = 5 + 5 + 5 + 5 = 20
Juan’s Work
5 Superscript 4 = 5 times 5 times 5 = 125

Answers

Aida’s work because 5 to the 4th power is 5x5x5x5=625

Answer:

A.

✔ Aida’s Work

Step-by-step explanation:

E 2021

PLEASE HELP ASAP! I WILL MARK BRAINLIEST IF YOU ARE RIGHT! The following dot plot shows the mass, in kilograms, of each of the 46 kittens adopted from an animal shelter last month. Each dot represents a different kitten.

Which of the following is a typical mass of one kitten?
Choose 1 Answer:
A: 1.8 Kilograms
B: 2.2 Kilograms
C: 3.8 Kilograms
D: 4.6 Kilograms

Answers

Answer:

1.8

Step-by-step explanation:

here u go <3

The mass of one kitten is 1.8 Kg

What is Mean?

Mean, median, and mode are the measures of central tendency, used to study the various characteristics of a given set of data. A measure of central tendency describes a set of data by identifying the central position in the data set as a single value. We can think of it as a tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendencies are Mean, Median, and Mode. Choosing the best measure of central tendency depends on the type of data we have.

The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

Mean = (12 + 34 + 45 + 50 + 24)/5

Mean = 165/5 = 33

Given:

Total kittens= 46

So,

Mean= Total mass/ number of kittens

mean= 0.8* + 1*3 + 1.2*4+ 1.4 * 6+ 1.6*8+ 1.8*8+ 2*7+ 2.2*5 + 2.4 * 2 + 2.6*1+3.8*1 / 46

=80.4/ 46

= 1.75

Learn more about mean here:

https://brainly.com/question/15323584

#SPJ2


In the school chorus,
5
20
of the students are fourth graders.

In simplest form, what fraction of the students in the school chorus are fourth graders?

Answers

Answer: 1/6

Step-by-step explanation:

Please help it’s due by the end of tonight and I’m not sure what to do if you can’t see (sorry I took a picture of my computer it’s a bit Glitched) you can zoom in

Answers

Do not click that link it’s a hacker please

edward deposited $6,000 into a savings account 4 years ago. the simple interest rate is 3% how much money did edward earn in interest?
(SHOW FULL WORK FOR BRAINLIEST) PLEASE HELP

Answers

Answer:

$6000×3%=180 for a month

so for for years

=6000x48×3%=R8 640

Step-by-step explanation:

1 year has 12 month so you will say 4 year's × 12 Month's it will give you 48 so you Multiply by his deposited money ×Percent

formula=Deposit money×Year's×Percent

A boat is 1000 meters from the base of a cliff. If the angle of depression from the top of the cliff to the boat is 15 degrees, how tall is the cliff? Round your answer to the nearest tenth

Answers

9514 1404 393

Answer:

  267.9 m

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

In this geometry, the angle of depression is the angle of interest. The "adjacent" side of the triangle is the distance to the boat. The "opposite" side is the height of the cliff.

  tan(15°) = height/(1000 m)

  height = (1000 m)tan(15°)

  height ≈ 267.9 m

The cliff is about 267.9 meters tall.


2. The angles of a pentagon are 6x, (2x + 20°),(3x - 20%), 2x and 14x. Find x. Please answer please please ​

Answers

Answer:

x=20

Step-by-step explanation:

The sum of two numbers is -25. One number is 101 less than the other. Find the numbers

Answers

Answer:

-63, 38

Step-by-step explanation:

1st number = x

2nd number = x+101

x+x+101=-25

2x=-126

x=-63

1st number = x = -63

2nd number = x+101 = 38

Answer:

x=38

y= -63

Step-by-step explanation:

x+y=-25

y=x-101

x+(x-101)= -25

2x=-25+101

2x=76

x=76/2

x=38

y=x-101

y=38-101

y= -63

Which of the following have the correct solution? Check all
that apply.
0 2x + 5 = 19; x = 7
3 + x + 2 - x = 16; x = 3
X +2
= 2; x=8
5
0 6 = 2x – 8; x = 7
14 = x +5; x = 18

Answers

Step-by-step explanation:

To do this, we will substitute the x values to their corresponding equations,

1)

[tex]2x + 5 \\ = 2(7) + 5 \\ = 14 + 5 \\ = 19[/tex]

Given 2x + 15 = 19

Calculated 2x + 15 = 19

Given = Calculated, this solution is correct.

2)

[tex]3 + x + 2 -x \\ = 3 + 3 + 2 - 3 \\ = 8 - 3 \\ = 5[/tex]

Given 3 + x + 2 - x = 16

Calculated 3 + x + 2 - x = 5

Given not equal to calculated, this solution is incorrect.

3)

[tex] \frac{x + 2}{5} \\ = \frac{8 + 2}{5} \\ = \frac{10}{5} \\ = 2[/tex]

Given (x+2)/5 = 2

Calculated (x+2)/5 = 2

Given = Calculated, this solution is correct.

4)

[tex]6 = 2x - 8 \\ 2x - 8 = 6[/tex]

[tex]2x - 8 \\ = 2(7) - 8 \\ = 14 - 8 \\ = 6[/tex]

Given 2x - 8 = 6

Calculated 2x - 8 = 6

Given = Calculated, this solution is correct.

5)

[tex]14 = \frac{1}{3} x + 5 \\ \frac{1}{3} x + 5 = 14[/tex]

[tex] \frac{1}{3} x + 5 \\ = \frac{1}{3}(18) + 5 \\ = \frac{18}{3} + 5 \\ = 6 + 5 \\ = 11[/tex]

Given 1/3x + 5 = 14

Calculated 1/3x + 5 = 11

Given not equal to Calculated, this solution is not correct.

Therefore the Correct solutions are 1,3 and 4.

28, 22, 16, 10,...
O Arithmetic
O Geometric
O Neither

Answers

Answer:

Arithmetic

Step-by-step explanation:

Sequences:

A sequence is called arithmetic if the difference between consecutive terms is the same.

A sequence is called geometric if the quotient between consecutive terms is the same.

In this question:

28 - 22 = 22 - 16 = 16 - 10 = ... = 6

Difference is always 6, that is, each term is the previous one subtracted by 6. So the sequence is arithmetic.

Let X and Y be the following sets:
X = {5, 10, 15}
Y = {3, 6, 9, 12, 15}
Which of the following is the set
XUY?

Answers

Answer:

XuY = { 3,5,6,9,10,12,15}

Answer choices
50%
60%
65%
If you put a link I will report

Answers

Answer:

50%

Step-by-step explanation:

what is the median of 16, 18, 18, 19, 25, 27, 28, 31, 31, and 32.

Answers

Answer:

26

Step-by-step explanation:

If the data is in order, the median is the middle value.

If there are two values in the middle, you add them together and divide by 2

So [tex]\frac{25+27}{2} =26[/tex]

26 because in between 25 and 27 is 26 any other numbers that’s missing is because it’s not the median

Find the value of x. Round to the nearest degree

Answers

Answer:

b. 44°

Step-by-step explanation:

Reference angle = x

Hypotenuse = 21

Adjacent = 15

Apply trigonometric function CAH:

[tex] Cos(x) = \frac{Adj}{Hyp} [/tex]

[tex] Cos(x) = \frac{15}{21} [/tex]

[tex] x = cos^{-1}(\frac{15}{21}) [/tex]

x = 44.4153086° ≈ 44° (nearest degree)

Use the remainder theorem and synthetic division to find f(k).
k= -1; f(x) = x² - 4x +5

Answers

Answer:

10

Step-by-step explanation:

i hope this helps you <3

which if the following equations fit this graph?​

Answers

y=3/2


That it I think so

Excuse me brainly, May i have your help..? I will give you the brainiest!

Determine the equation for the line of best fit to represent the data.

scatter plot with points going down from about zero comma 4 to the right to about 7 comma zero

y equals two thirds times x plus 4
y equals negative two thirds times x plus 4
y equals negative three halves times x plus 4
y equals negative two thirds times x minus 4

Answers

I think the answer would be negative Y equals 4 and the reason why is because

Help please and show the steps

Answers

9514 1404 393

Answer:

  4096∠0°

Step-by-step explanation:

The polar form of the base value is 2∠120°. Then the 12-th power is ...

  (2^12)∠(12×120°) = 4096∠0° . . . . or θ = 0 radians, as you wish

_____

I prefer the simpler notation r∠θ, rather than ...

  r(cos(θ) +i·sin(θ))   or   r·cis(θ)   or   r·e^(iθ)

You might not see this notation very often in areas outside of electrical engineering.

Is Anyone know the answer????

Answers

Answer:

Angle 1 = 40

Step-by-step explanation:

Angle 1 and Angle 2 are alternate angles. So,

2x + 20 = 3x + 10

3x - 2x = 20 - 10

x = 10

Angle 1 = 2x + 20 = 2 x 10 + 20 = 40

Help plz I will give brainliest

Answers

B 4cup of sugar and 3cups of flour =1cup of sugar and 3/4 cup of flower

A family buys 6 airline tickets online. The family buys travel insurance that costs ​$18 per ticket. The total cost is ​$1,056. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.

Answers

Answer:

let x represent the number tickets

number of ticket=6

cost of the travelling insurance per ticket =$18

total cost= $1056

(x+x+x+x+x+x+18)= $1,056

6x + 18 = $1,056

For every 9 pounds of blueberries that Joey picks, she
is able to bake 6 blueberry pies. How many pounds of
blueberries does Joey use in each pie?

Answers

1.5 pounds of blueberry in each pie

Explanation:
So its basically asking for the unit rate of blueberry per pie.
To solve that, we divide 9 by 6
9 divided by 6 is 1.5, which will mean that there are 1.5 pounds of blueberries in one pie.

Now, DONT do it the other way around (6 divided by 9) BECAUSE, if you do that, you will end up solving the pie per blueberry (which in that case is, ur gonna find how many pie you can make for 1 blueberry) so uhh therr ya go. Hope this helps
Marm me brainliest pls-

Solve the following inequality for z. Write your answer in simplest form.
3z – 4 > 8z + 2

Answers

Answer:

I think question is wrong

Step-by-step explanation:

3z-4>8z+2

3z-4+4>8z+2+4

3z>8z+6

[tex] \frac{3}{3} z > \frac{8z + 6}{3} \\ z > 8z + 2[/tex]

how many square feet is in a acre

Answers

43,560 is the answer
43560 square feet in an acre

A total of 255 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold? answer ASAP will give brainliest!!!

Answers

Answer:

85

Step-by-step explanation:

255 ÷ 3 = 85

85×2= 170 This is how much student tickets were sold.

255 - 170= 85

85 adult tickets were sold.

PLEASE HELP! 20 POINTS!!

Answers

Answer:

15

Step-by-step explanation:

In this problem we need to use the numbers given. So in the problem it states that k = 20 and v = 10. We can replace the letters in the equation for the numbers that it equals so the equation can make sense so 25 - 20 + 10 because k is 20 and v is 10 I simply just replaced the letters with the numbers given in the problem. Then we can just subtract 25 - 20 which is 5 and add 10 which leaves you at a final answer of 15. Hope this helped!

PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ?

Answers

Answer:

vertical angles

Step-by-step explanation:

bc they are across from eachother

A rectangular prism has a length of 11 centimeters, a height of 18 centimeters, and a width of 11 centimeters. What is its volume, in cubic centimeters?

Answers

Answer:

2,178

Step-by-step explanation:

Multiply all the numbers together in other words do the length of the base times the width of the base then multiply the product by the height of the prism.

(11)(11)18

If x = 2 and y = 4, what is 6x - 5y?

Answers

Answer:

-8

Step-by-step explanation:

6(2) = 12

5(4) = 20

12-20

-8

Answer:

44

Step-by-step explanation:

(6x4)+(5x4)= 44

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