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
Andrei [34K]
2 years ago
9

The article "Measuring and Understanding the Aging of Kraft Insulating Paper in Power Transformers" (IEEE Electrical Insul. Mag.

, 1996: 28–34) contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain range:(a) Construct a boxplot of the data and comment on any interesting features. (b) Is it plausible that the given sample observations came from a normal distribution? Explain and provide any associated graphs. (c) Calculate a two-sided 95% confidence interval for the true average degree of polymerization. (d) Does the interval suggest that 440 is a plausible value for the true average degree of polymerization? Explain. (e) Does the interval suggest that 450 is a plausible value for the true average degree of polymerization? Explain

Mathematics
1 answer:
givi [52]2 years ago
3 0

Answer:

Step-by-step explanation:

Hello!

You have the data corresponding to 17 observations on the degree of polymerization for paper specimens whose viscosity times concentration fell in a certain range.

a) Boxplot attached.

Box: The 2 quantile (Me) appears to be in the middle of the box, the distance between the 1st quantile and the second quantile appears to be equal than the distance between the 2nd quantile and the 3rd quantile. The mean (black square) is greater than the 2nd quantile. In general, the distribution inside the box appears to be symmetrical (comparing just the Me<X[bar], perhaps slightly right-skewed)

Whiskers: The upper whisker is approximately twice as long as the lower whisker. There are no visible outliers in the data set.

In general, it appears as if the data set is right-skewed.

b) I would be more comfortable with a more symmetrical boxplot, but this one shows enough symmetry to be able to assume that the variable may have a normal distribution.

c) If we assume the normal distribution of the variable, you can use a student t to estimate the true value of the average degree of polymerization of paper:

[X[bar] ± t_{n-1;1-\alpha /2} * \frac{S}{\sqrt{n} }]

95% CI: t_{16;0.975}= 2.120

X[bar]= 438.29

S= 15.14

[438.29 ± 2.120 * \frac{15.14}{\sqrt{17} }]

[430.47;446.03]

With a 95% confidence level, you'd expect the interval [430.47;446.03] to include the true value of the average degree of polymerization of paper.

d) and e)

For these two items, you have to use the calculated CI in c) to decide whether or not there is significant evidence to conclude that two possible values of μ are plausible.

To decide over a hypothesis test using a CI several conditions should be met:

1) The hypothesis has to be two-tailed, and for the same parameter estimated in the interval

2) Both the CI and the Hypothesis test should have complementary levels, this means that if the CI was made using a confidence level of 1 - α= 0.95, then the test should have a significance level of α= 0.05

If these conditions are met, the decision rule is:

If the interval doesn't include the value of the parameter stated in the null hypothesis, then you reject the null hypothesis.

If the interval includes the value of the parameter stated in the null hypothesis, then you do not reject the null hypothesis.

d) μ=440?

Hypothesis:

H₀: μ = 440

H₁: μ ≠ 440

α: 0.05

95% CI: [430.47;446.03]

440 is included in the interval, the decision is to not reject the null hypothesis.

Using a 5% significance level, there is significant evidence to conclude that the population mean of the degree of polymerization of paper is 440.

e) μ=450?

H₀: μ = 450

H₁: μ ≠ 450

α: 0.05

95% CI: [430.47;446.03]

450 is not included in the interval, the decision is to reject the null hypothesis.

At a level of 5%, the decision is to reject the null hypothesis, this means that the population mean of the degree of polymerization of paper is different than 450.

I hope it helps!

You might be interested in
Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK
lesantik [10]
Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2

==============================================

Explanation:

For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval

In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ] 
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank

-------------------------------------------

To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.

-------------------------------------------

Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4

This is why f(-4) = -3

-------------------------------------------

We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.

From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]

We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3

Doing those replacements and simplifying leads to...

[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2

So the average rate of change is 2

Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.

6 0
3 years ago
Convert the decimal to a fraction in simplest form. 0.25 =
Yuliya22 [10]
The answer in simplest form is 1/4.
4 0
3 years ago
Read 2 more answers
PLEASE HELP ME ASAP
velikii [3]

Answer:

Radius r=0.30m, Velocity, v=36m/s

(a) angular speed w=

r

v

=

0.3

36

=120rad/s

(b) final angular speed w

′

=0

From rotational kinematics w

′

2

−w

2

=2αθ

0−14400=2α×40×2π

⇒α=

160π

−14400

=−28.6rad/s

2

'Distance covered

=40×2πr

=40×2π×0.3=75.39m

5 0
2 years ago
4) What is the total cost (tax and price) on a purchase of $108.50 if the sales tax is 8%?
vitfil [10]
Answer: C)$117.18

$108.50 X 1.08 = $108.50
4 0
2 years ago
250% of a number is 60. What is the number
katrin [286]

60 / 2.50 = 24

the number is 24

7 0
2 years ago
Read 2 more answers
Other questions:
  • A man buys 12 shirts at $24.69 each. There is a 6% sales tax. Find his bill.
    7·2 answers
  • PLEASE HELP ME ASAP..........
    15·2 answers
  • How can patterns be used to determine products of a number and a power of 10?
    8·2 answers
  • 16.<br>(a)<br>Simply<br>3b + 5b - 2<br>​
    14·1 answer
  • Andy cut a tuna sandwich and a chicken sandwich into a total of 21 same size-pieces.He cut the tuna sandwich into 15 more pieces
    9·2 answers
  • A recipe uses 2.5 cups of flour to make 2 dozen cookies. if pamela wants to make 72 cookies, how many cups will of flours will s
    12·1 answer
  • If f(x) = 16x - 30 and g(x) = 14x - 6, for which value of x does (f - g)(x) = 0?
    10·1 answer
  • What are the x-intercept and the y-intercept of the graph of y=−1/2x−5
    7·2 answers
  • Y = -3x + 1 <br> What is the slope?
    13·2 answers
  • State the property.<br> power property of exponents.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!