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
Furkat [3]
3 years ago
5

A consumer agency is investigating the blowout pressures of Soap Stone tires. A Soap Stone tire is said to blow out when it sepa

rates from the wheel rim due to impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 29 Soap Stone tires were inflated to the recommended pressure, and then forces measured in foot-pounds were applied to each tire (1 foot-pound is the force of 1 pound dropped from a height of 1 foot). The customer complaint is that some Soap Stone tires blow out under small-impact forces, while other tires seem to be well made and don't have this fault. For the 29 test tires, the sample standard deviation of blowout forces was 1358 foot-pounds.
(a) Soap Stone claims its tires will blow out at an average pressure of 26,000 foot-pounds, with a standard deviation of 1020 foot-pounds. The average blowout force is not in question, but the variability of blowout forces is in question. Using a 0.1 level of significance, test the claim that the variance of blowout pressures is more than Soap Stone claims it is.
Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimating σ2 or σ, F test for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.
(ii) Find the sample test statistic. (Use two decimal places.)
(iii) Find the P-value of the sample test statistic. (Use four decimal places.)
(b) Find a 99% confidence interval for the variance of blowout pressures, using the information from the random sample. (Use one decimal place.)
Mathematics
1 answer:
Likurg_2 [28]3 years ago
3 0

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: Impact force needed for Sap Stone tires to blow out. (foot-pounds)

n= 29, S= 1358 foot-pound

a)

Soap Stone claims that "The tires will blow out at an average pressure of μ= 26000 foot-pounds with a standard deviation of σ= 1020 foot-pounds.

According to the consumer's complaint, the variability of the blown out forces is greater than the value determined by the company.

I)

Then the parameter of interest is the population variance (or population standard deviation) and to test the consumer's complaint you have to conduct a Chi-Square test for σ².

σ²= (1020)²= 1040400 foot-pounds²

H₀: σ² ≤ 1040400

H₁: σ² > 1040400

α: 0.01

II)

X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}

X^2_{H_0}= \frac{(n-1)S^2}{Sigma^2}= \frac{(29-1)*(1358)^2}{1040400} = 49.63

III)

This test is one-tailed to the right and so is the p-value. This distribution has n-1= 29-1= 28 degrees of freedom, so you can calculate the p-value as:

P(X²₂₈≥49.63)= 1 - P(X²₂₈<49.63)= 1 - 0.99289= 0.00711

⇒ The p-value is less than the significance level so the test is significant at 1%. You can conclude that the population variance of the blowout forces is less than 1040400 foot-pounds², at the same level the population standard deviation of the blow out forces is less than 1020 foot-pounds.

b)

99% CI for the variance. Using the X² statistic you can calculate it as:

[\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ]

X^2_{n-1;\alpha /2}= X^2_{28; 0.005}= 13.121

X^2_{n-1;1-\alpha /2}= X^2_{28; 0.995}= 49.588

[\frac{28*(1358)^2}{49.588} ;\frac{28*(1358)^2}{13.121} ]

[1041312.253; 3935415.898] foot-pounds²

I hope this helps!

You might be interested in
I NEED THIS ANSWERED AS SOON AS POSSIBLE! How much material is needed to construct a triangular tent that is 6 feet wide, 4 feet
Elena-2011 [213]

To figure out this problem, you need to find the surface area of a triangular prism.

a=5ft

b=5ft

c=6ft

h=8ft

A= (a*h) + (b*h) + (c*h) + 1/2√-a⁴ + 2(a*b)² + 2(a*c) - b⁴ + 2(b*c) - c⁴

=152 square feet

5 0
3 years ago
Need help with this pls show work
Gemiola [76]

Answer:

Ron got 3 additional toppings

Step-by-step explanation:

Lets call the amount of toppings that Ron got t. With this, we can set up the following equation:

8.95+0.65t=10.90

Subtract 8.95 from both sides:

0.65t=1.95

Divide both sides by 0.65:

t=3

Hope this helps!

6 0
3 years ago
Read 2 more answers
6 1/5 + (-7 3/5)
GREYUIT [131]
Since you are subtracting a negative you can do it this way. do 7 3/5 - 6 1/5. that leaves you with 1 2/5. so in the end you will have -1 2/5
5 0
2 years ago
I need to know the answer to this
scoundrel [369]
The answer is x=−1.3125

I hope this helps. 

Have a "AWESOME" day! :)
<span>
</span>
8 0
3 years ago
Read 2 more answers
The graph shows one of the linear equations for a system of equations. Which equation represents the second linear equation for
erastova [34]

Answer:

  C)  2/3x + 3y = 3

Step-by-step explanation:

The attached graph shows only choice C intersects the desired point.

Essentially, the given graph is irrelevant. What you want to know is which equation has (3/4, 5/6) as a solution.

There are at least a couple of ways you can figure this out:

  1. try the given point in the equations to see which one works
  2. examine the features of the given equations to see which might work

__

If we consider the second approach, we realize all of the equations have negative y-intercepts except choice C*. For an equation with a negative y-intercept to be the solution, the x-intercept must be less than 3/4. That is not the case for any of choices A, B, or D, leaving only choice C as a viable possibility.

We can check to see if the given point satisfies choice C. Filling in for x and y, we get ...

  (2/3)(3/4) + 3(5/6) = 2/4 +5/2 = 3 . . . . . . the point is on this line

_____

In the attached graph, choice C is the black line.

_____

* For an equation of the form ax+by=c, the y-intercept is c/b and the x-intercept is c/a. The sign of the quotient can be figured from the signs of a, b, and c without doing any division.

_____

<em>Comment on intercepts</em>

Considering the signs and values of the x- and y-intercepts can tell you a lot about the solution to a system of equations. They tell you where the line segment between the axes lies, and they can give you a clue as to the location (quadrant) of the intersection point of two lines. Often, the intercepts are all you need to create a useful graph of an equation.

5 0
3 years ago
Other questions:
  • What is the length between (4,3) and (-5,-2)
    15·2 answers
  • Solving radical equations<br> How to solve radical equations
    14·2 answers
  • Macy is making a border out of strips of wall boarder placed end to end along the 12-foot wall in her room. Each strip is foot l
    15·1 answer
  • this week you read 57 pages. this is seven more than two times the number of pages read last week. write an equation and solve.
    13·1 answer
  • Is -1 1/2 rational?
    9·2 answers
  • Find the solution set for the equation.<br> |7x - 5] +5=14
    6·2 answers
  • A cookie recipe calls for 1 2/3 of sugar if you plan on changing the recipe to make it 2 1/2 times as much how many cups of suga
    15·1 answer
  • ∠A and ∠B are complements. If the measure of angle A=(8x-23) and the measure of angle B=(7x-7), then find the measure of ∠A
    9·1 answer
  • Marty saved $200 this month. That is 50% of the money he earned mowing lawns. How much money did Marty earn mowing lawns? dollar
    15·1 answer
  • Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island o
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!