Two random samples 4. 49, 7. 68, 5. 97, 0. 97, 6. 88, 6. 07, 03. 08, 04. 02, 03. 83, 6. 35, and 4. 59, 3. 39, 3. 79, 6. 89, 5. 07, 07. 41, 0. 44, 2. 47, 4. 80, 7. 23 were obtained independently from distributions with the same mean. Perform a permutation test to test the hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population. As a test statistic use: (i) The difference of sample ranges. (ii) The ratio of sample variances. (iii) Compare both results
Answers
A. Main Answer:
The hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population, we can perform a permutation test using two different test statistics:
(i) the difference of sample ranges and
(ii) the ratio of sample variances. By comparing the results of both test statistics, we can draw conclusions about the variability in the populations.
(i) Difference of Sample Ranges:
1. Calculate the sample range for each sample. The sample range is the difference between the maximum and minimum values in the sample.
Sample 1 Range = Maximum value - Minimum value for Sample 1
Sample 2 Range = Maximum value - Minimum value for Sample 2
2. Calculate the observed difference of sample ranges, which is the difference between the sample range of Sample 2 and Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the difference of sample ranges for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the difference of sample ranges under the null hypothesis (where variability is the same in both populations).
6. Compare the observed difference of sample ranges from step 2 with the distribution obtained from the permutations.
(ii) Ratio of Sample Variances:
1. Calculate the sample variance for each sample.
2. Calculate the observed ratio of sample variances, which is the ratio of the sample variance of Sample 2 to the sample variance of Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the ratio of sample variances for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the ratio of sample variances under the null hypothesis.
6. Compare the observed ratio of sample variances from step 2 with the distribution obtained from the permutations.
By comparing the results of both test statistics, we can assess whether the variability in the second population is significantly larger than the first population. If both test statistics consistently indicate larger variability in the second population, it provides evidence against the null hypothesis and suggests that the variability in the second population is indeed larger.
To know more permutation test , refer here :
https://brainly.com/question/21083287#
#SPJ11
Related Questions
What is the minimum of the data?
0
5
7
13
Answers
Answer:
b; [5]
Step-by-step explanation:
i took the quiz
After a discount of 20 %, Marjorie paid $ 180 for a dress. The original price of the dress was
Answers
=============================================
Explanation:
x = original price
If she saves 20%, then she still pays the remaining 80% which then converts to the decimal form 0.80
The expression 0.80x represents the new price, or sale price, of the dress. We're told this price is $180
Equate the two expressions and solve for x
0.80x = 180
x = 180/0.80
x = 225
The original price is $225
------------------------
Checking the answer:
20% of 225 = 0.20*225 = 45
She saves $45
225 - 45 = 180
This confirms the answer.
Factor completely 4xy 9x 24y 54. (4y − 9)(x − 6) (4y − 9)(x 6) (4y 9)(x − 6) (4y 9)(x 6).
Answers
Answer:
(4y + 9)(x + 6)
Step-by-step explanation:
Attached photo for proof its right
A function in which the points on the graph are not connected is called a(n)
Answers
Answer:
discontinuous
Step-by-step explanation
Please help me if you know, I would appreciate if you could explain how to do this!
In the figure, the area of the shaded region is 299π cm²
What are the exact areas of the inner and outer circles?
Also, the answers need to be in cm^2
Answers
Answer:
See answers below
Step-by-step explanation:
Entire outer circle area = pi r^2 = pi 18^2 = 324 pi cm^2
if you subtract the small unshaded circle you get 299 pi
324 pi - smaller circle = 299 pi
smaller circle = 25 pi cm^2
If the diameter in the semicircle is 10.5 what is the perimeter
Answers
Answer:
Perimeter of semi-circle = 16.5 cm.
Step-by-step explanation:
Given that,
Diameter of the semi-circle, \(\text{d} = 10.5 \ \text{cm}\)
So, Radius of the semi-circle, \(\text{r} = 10.5\div2 \ \text{cm}\)
We know that,
Perimeter of a Circle \(= 2\pi r\)
So, Perimeter of a semi-circle \(= \dfrac{1}{2} \times 2\pi r\)
\(= \pi r\)
\(= \dfrac{22}{7} \times 10.5\div2\)
\(= 16.5 \ \text{cm}\)
Hence, Perimeter of the semi-circle with diameter 10.5 cm is 16.5 cm.
help 6th grade math i will give brainliest
Answers
Please I need HELP
Multiply the following polynomials. The solution must be in standard form.
(-3m2 – 3m) (-3m4 +
3m3
+
m2 + m)
0 -9m + 9m4 + 9m2 – 9
O 9m
9m4 - 6m3 – 3m
9m
12m4 – 6m² – 3m?
6
O 9m
12m4
3m3
Answers
9514 1404 393
Answer:
\(\text{(c)} \quad 9m^6-12m^4-6m^3-3m^2\)
Step-by-step explanation:
As is often the case with multiple choice questions, you only need to identify a feature of the answer set that distinguishes right from wrong. Here, that can be the lowest-power term, which is always the product of the lowest-power terms.
That product is (-3m)(+m) = -3m². This matches the third answer choice.
\(9m^6-12m^4-6m^3-3m^2\)
A local church has a total population consisting of 480 adult members. The church's administrators would like to estimate the average weekly donation per member per week. A random sample of 65 members was found to have an average donation of $50.40. Further, the population standard deviation is $12.30. The 95% confidence interval to estimate the average weekly donation is ________. Hint: don't forget the finite population correction factor.
Answers
The 95% confidence interval to estimate the average weekly donation per member is approximately $47.42 to $53.38.
To calculate the 95% confidence interval for the average weekly donation per member, we can use the following formula:
Confidence interval = Sample mean ± (Critical value) × (Population standard deviation / √(Sample size))
First, we need to determine the critical value corresponding to a 95% confidence level. Since the sample size is relatively large (n > 30), we can use the Z-distribution. The critical value for a 95% confidence level is approximately 1.96.
Next, we can substitute the given values into the formula:
Sample mean = $50.40
Population standard deviation = $12.30
Sample size = 65
Using these values, we can calculate the confidence interval:
Confidence interval = $50.40 ± (1.96) × ($12.30 / √(65))
Calculating the value inside the parentheses:
($12.30 / √(65)) ≈ $1.52
Substituting this value into the formula:
Confidence interval = $50.40 ± (1.96) × $1.52
Calculating the values outside the parentheses:
$1.96 × $1.52 ≈ $2.98
Substituting this value into the formula:
Confidence interval ≈ $50.40 ± $2.98
Therefore, the 95% confidence interval is $47.42 to $53.38.
Learn more about confidence intervals at
https://brainly.com/question/32546207
#SPJ4
What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Answers
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
for such more question on Domain
https://brainly.com/question/16444481
#SPJ8
Nicole drove 275 miles in 5 hours. At the same rate, how long would it take her to drive 605 miles?
Answers
Answer:
i think its 12 hours
Step-by-step explanation:
use calculator
a. If α is assigned the value 0.001, what are we saying about the type I error?
b. If α is assigned the value 0.05, what are we saying about the type I error?
c. If α is assigned the value 0.10, what are we saying about the type I error?
Answers
(a) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.
(b) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.
(c) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.
What is Type I error of α the value 0.001,?a. If α is assigned the value 0.001, we are setting a very low significance level for the hypothesis test. This means that we are willing to accept only a very small probability of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.
What is Type I error of α the value 0.05?b. If α is assigned the value 0.05, we are setting a standard significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.05 or 5% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.
What is Type I error of α the value 0.10?c. If α is assigned the value 0.10, we are setting a relatively high significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.10 or 10% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.
Learn more about hypothesis test
brainly.com/question/30588452
#SPJ11
Quadrilateral ABCD is translated 7 units down and 2 units to the right.
The length of side AB of the original quadrilateral is
units. After the translation, the length of side AB will
.
Answers
ABCD is a quadrilateral that has been translated 2 units to the right and 7 units down. The length of side AB will not change following the translation. Option C is correct.
What is translation?Each point in a figure is moved the same distance in the same direction using a sort of transformation known as translation.
The complete question is
"Quadrilateral ABCD has translated 7 units down and 2 units to the right.
The length of side AB of the original quadrilateral is_____ units. After the translation, the length of side AB will___________ .
2
3
3.5
4
----------------------------
Increase
Decrease
Remain the same"
Quadrilateral ABCD has translated 7 units down and 2 units to the right. After the translation, the length of side AB will remain the same.
Hence option C is correct.
To learn more about the translation refer;
https://brainly.com/question/11914505
#SPJ1
Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?
A
P will be closer to A because it
distance from A to B.
P will be closer to A because it will
the distance from A to B.
O P will be closer to B because it will be
the distance from B to A.
P will be closer to B because it will be
the distance from B to A.
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
A.
Step-by-step explanation:
Given that point P partitions a directed line segment from A to B into the ratio 3:4, we are to determine how close P is to either A or B.
To do this, we take an example.
Let the length of line segment AB be 14 Units.
Since P divides AB in the ratio 3:4
Length of AP\(=\frac{3}{7}X14=6 \:units\)Length of PB\(=\frac{4}{7}X14=8 \:units\)Therefore, from the above, we can conclude that P will be closer to A as its distance from A is shorter than its distance from B.
The correct option is A.
Answer:
Point P partitions the directed line segment from A to B into the ratio 3:4. Will P be closer to A or B? Why?
A number line goes from point A to point B. A line is drawn from point A to point B.
Right Answer A.) P will be closer to A because it will be Three-sevenths the distance from A to B.
Wrong Answer B.) P will be closer to A because it will be Four-sevenths the distance from A to B.
Wrong Answer C.) P will be closer to B because it will be Three-sevenths the distance from B to A.
Wrong Answer D.) P will be closer to B because it will be Four-sevenths the distance from B to A.
Step-by-step explanation:
describe what happens to the mean, the standard deviation, and the shape of a distribution when all of the scores are transformed into z-scores.
Answers
The distribution will keep the same shape as the original, the standard deviation will be 1 and it will have a mean 0
What is meant Standard Deviation?Standard Deviation: the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range
it is asked that, to describe what happens to the mean, the standard deviation, and the shape of a distribution when all of the scores are transformed into z-scores
Every score stays in the exact same position relative to every other score in the distribution. Mean - when raw scores are transformed into z-scores, the mean will always = 0. The standard deviation - when any distribution of raw scores is transformed into z-scores the standard deviation will always = 1
to learn more about Standard Deviation visit:
brainly.com/question/14747159
#SPJ4
A shopkeeper bought articles at $4.00 a dozen and sold them at 4.50 a dozen her percentage profit was
Answers
Answer:
12.5
Step-by-step explanation:
Find the profit ( 4.50- 4) And then profit over original price multiplied by 100 ( 0.50/4×100)An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P = -2²+ 17t + 180, where 1 st≤ 6. Find the day that 210 students had the flu. Recall that the restriction on this at most 6.
Submit Answer
Answers
Answer:
At the 3rd day 160 students caught flu.
Step-by-step explanation:
Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6
The total number of students is represents by P.
We need to find the day that 160 students had the flu.
Substitute the value of P=160 in above formula.
Hence the value of t=10 or t=3
But it is given that 1 ≤ t ≤ 6, Therefore select t=3
Hence, at the 3rd day 160 students caught flu.
A blueberry pie is made of 10 inch diameter pie pan.the pie is cut into 8 equal slides.what is the area of 1 slice
Answers
Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.
What is diameter?In a circle, diameter is a line that passes through the center and meets the circumference at opposite ends. It is twice as long as that of the radius of the circle. In other words, the diameter of a circle is the line that passes through the center and divides the circle into two equal parts. Let us learn more about diameter definition and properties in this article.The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.To learn more about diameter refer to:
https://brainly.com/question/23220731
#SPJ1
a type of medicine is given in a 100 miligram dosage. the medicine comes in a 12 gram bottle. how many 100 milligram doses are in a bottle?
Answers
The medicine bottle has 120 doses of 100 miligram each.
As per the known fact, 1000 miligram is 1 gram. So, the amount of medicine in the bottle in milligrams = 12×1000
Performing multiplication on Right Hand Side of the equation
Amount of medicine in bottle = 12000 milligrams.
Now, number of dose of 100 miligram medicine = 1
Amount of dose of 12000 miligram medicine = (1/100)×12000
Performing division and multiplication on Right Hand Side of the equation
Amount of doses in 12000 miligram medicine = 120
Thus, there are 120 doses in a medicine.
Learn more about dosage calculations -
https://brainly.com/question/24793154
#SPJ4
At his job Lee earns $400 per week plus a 6% commission on his sales. He wants to earn at least $550 this week. Which of the following represents this situation?
Answers
Answer:
Your answer is: $500
You have to add \(400+.06x=500\)
Step-by-step explanation:
Hope this helped : )
All three sides and all three angles are equal in an equilateral triangle. Could this figure
also be a parallelogram?
never
always
sometimes
Answers
Answer:
never
Step-by-step explanation:
Any triangle can never be a parallelogram because it only has three sides.
quadrilateral with parallel sides is a parallelogram.
HELP HAVING BAD DAY!!!!
A securities broker advised a client to invest a total of $21,000 in bonds
paying 12% interest and in certificates of deposit paying 51% interest. The
annual income from these investments was $2250. Find out how much was
invested at each rate.
Answers
According to the given information, the total amount invested is $21,000, so we have the equation:
x + y = 21,000
The annual income from these investments is $2250, which can be expressed as the sum of the interest earned from each investment:
0.12x + 0.51y = 2250
Now, we have a system of two equations:
x + y = 21,000
0.12x + 0.51y = 2250
We can solve this system of equations to find the values of x and y, representing the amounts invested in bonds and certificates of deposit, respectively.
One way to solve this system is by substitution or elimination. In this case, let's use the elimination method:
Multiplying the first equation by 0.12 to make the coefficients of x in both equations the same, we have:
0.12x + 0.12y = 2520
Subtracting this equation from the second equation, we eliminate x:
0.51y - 0.12y = 2250 - 2520
0.39y = -270
y = -270 / 0.39
y ≈ -692.31
Since we cannot have a negative investment, this suggests an error or inconsistency in the given information or calculations.
Please double-check the provided values or calculations, as they currently do not yield a feasible solution.
Jennifer's family is going to see the Atlanta Symphony Orchestra. Tickets cost $79 each, and there is a $14.95 convenience fee for each ticket. If Jennifer's mom buys tickets for 6 people, how much money does she spend in all?
Answers
Answer:
563.7
Step-by-step explanation:
add 79 + 14.95 and multiply that by 6
A house was purchased in 2012 for $150,000 If the value of the home increases by 3% each year, what will the house be worth in the year 2015?
Answers
Can someone help me plz :)
Answers
Answer:
4
4
4
4
Step-by-step explanation:
the melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in a sample mean of 94.32. assume the distribution of melting point is normal with a population standard deviation of 1.20. does the true mean melting point differ from 95? use a significance level of 0.01
Answers
We do not have enough evidence to conclude that the true mean melting point differs from 95 at a significance level of 0.01.
To determine if the true mean melting point differs from 95, we can use a one-sample t-test with a significance level of 0.01.
The null hypothesis is that the true mean melting point is equal to 95, and the alternative hypothesis is that the true mean melting point is different from 95.
We can calculate the t-statistic using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
where sample size is 16, sample mean is 94.32, hypothesized mean is 95, and sample standard deviation is the same as the population standard deviation of 1.20.
Plugging in these values, we get:
\(t = (94.32 - 95) / (1.20 / \sqrt{(16)} ) = -2.6667\)
Using a t-distribution table with 15 degrees of freedom (n-1=16-1), and a two-tailed test at a significance level of 0.01, the critical t-value is ±2.947.
Since our calculated t-value of -2.6667 falls within the acceptance region (-2.947 < -2.6667 < 2.947), we fail to reject the null hypothesis.
For similar question on standard deviation.
https://brainly.com/question/31358088
#SPJ11
Solve the system of equations by the substitution method
{y=3x+8
{y=5x+9
Answers
Answer:
(x, y) (-1/2, 13/2)
Step-by-step explanation:
since y is both equal to these eqaution we can set the equation eqaul together.
3x+8=5x+9
2x = -1
x = -1/2
y = 3(-1/2) + 8
y = 13/2
i have no idea how to do these. please help me solve #9-11
Answers
Answer: i am not good at this but i think it is this
Step-by-step explanation:
umm it mit be #0-
which table and graph represent the equation y =5x
Answers
No table and graph given for us to choose from.
Find the slope of the line
Answers
Answer:
1/5th
Step-by-step explanation:
trust me. ik how to do slopes