1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
n200080 [17]
3 years ago
9

An article in the Journal of Materials Engineering (Vol 11, No. 4, 1989, pp. 275-282) reported the results of an experiment to d

etermine failure mechanisms for plasma-sprayed thermal barrier coatings. The failure stress for one particular coating (NiCrAlZr) under two different test conditions is as follows:
Failure stress ( times 10^6 Pa) after nine 1-hr cycles: 19.8, 18.5, 17.6,16.7, 16.7, 14.8, 15.4, 14.1, 13.6
Failure stress ( times 10^6 Pa) after six 1-hr cycles: 14.9, 12.7, 11.9, 11.4, 10.1,7.9
(a) What assumptions are needed to construct confidence intervals for the difference in mean failure stress under the two different test conditions? Use normal probability plots of the data to check these assumptions.
(b) Perform a hypothesis test to determine if the mean failure stress of the two different test conditions is the same at the 0.05 significance level.
(c) Confirm that the P-value of this test is 0.001.
Mathematics
1 answer:
RSB [31]3 years ago
6 0

Answer:

Step-by-step explanation:

Hello!

You have two variables of interest

X₁: failure stress of a NiCrAlZr coating after nine 1-hr cycles.

X₂: failure stress of a NiCrAlZr coating after six 1-hr cycles.

a)

To be able to estimate the difference between the means using a confidence interval, you need that both variables have a normal distribution and to determine whether or not the population variances are equal.

If the population variances are equal, σ₁²=σ₂², you can use a pooled variance t-test

If the population variances are different, σ₁²≠σ₂², you have to use Welch's t-test

Using α: 0.05

The normality test for X₁ shows a p-value of 0.7449 ⇒ You can assume it has a normal distribution.

The normality test for X₂ shows a p-value of 0.9980 ⇒ You can assume it has a normal distribution.

The F-test for variance homogeneity shows a p-value of 0.6968 (H₀:σ₁²=σ₂²) ⇒You can assume both population variances are equal.

b) and c)

You need to test if both population means are the same, the hypotheses are:

H₀: μ₁=μ₂

H₁: μ₁≠μ₂

α: 0.05

t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}

Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{8*4.28+5*5.62}{9+6-2} }= \sqrt{4.7953}= 2.189= 2.19

t_{H_0}= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } = \frac{(16.36-11.48)-0}{2.19*\sqrt{\frac{1}{9} +\frac{1}{6} } } = 4.23

The distribution of this test is a t with 13 degrees of freedom and the test is two-tailed, so to calculate the p-value you have to do the following:

P(t₁₃≤-4.23)+P(t₁₃≥4.23)= P(t₁₃≤-4.23)+[1-P(t₁₃<4.23)]=  0.000492 + (1-0.999508)= 2*0.000492= 0.000984≅ 0.001

The p-value: 0.001 is less than α: 0.05, the decision is to reject the null hypothesis.

I hope it helps!

You might be interested in
Which expressions are equivalent to the one below? Check all that apply.
Paha777 [63]

Answer:

The answer is C.

Step-by-step explanation:

You have to apply Logarithm Law,

log( {a}^{n} ) \:  ⇒ \: n log(a)

So for this question :

log( {10}^{3} )  = 3 log(10)

8 0
3 years ago
What is the measure of A
Art [367]

Answer:

66+x=180°

=180°-66°

=114°

4 0
3 years ago
Fast Freddie is a widget assembler. He is paid $3.27 for every widget he assembles. What is Freddie's total pay for a week in wh
Brums [2.3K]
If he is paid 3.27 for every widget assembled...and he assembles 209...then his total pay for the week is : 3.27 * 209 = $ 683.43 <==
3 0
3 years ago
Read 2 more answers
The United States Postal Service charges a
lions [1.4K]

Answer:

your answer would to your question is d

6 0
3 years ago
31 gallons of gas cost $82.15.
Nadya [2.5K]
82.15 / 31 = 2.65 per gallon
8 0
3 years ago
Other questions:
  • M is the midpoint of CF for the point c(3, 4) and f (9, 8) find MG
    11·1 answer
  • brian made 16 paper cranes in 15 minutes.If he continues making cranes at this rate,how many cranes would he make in 2 hours?
    15·1 answer
  • 11. <br>2(9x + 15)- 2(8 + 2x) <br><br>12.<br>(7x - 12) - 2(3x + 10) <br><br>Help pls
    10·1 answer
  • How do i solve this equation for x? 6e^2x=7e^4x
    14·1 answer
  • Find the arc length of a partial circle
    8·2 answers
  • PlZz AnsWeR<br>If each quadrilateral below is a rectangle, find the missing measures. ​
    7·1 answer
  • Can someone help? Solve for x
    9·1 answer
  • A python snake on display at a pet store is 62 centimeters long. About how many inches long is the snake? Using
    15·1 answer
  • I tried my best to study for a test that is due in 2 days but I just am not great at math what so ever can anyone help?
    9·1 answer
  • PLEASE HELP 10 POINTS!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!