Recent questions in Research Methodology

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Keegan Stevens 2023-03-25

In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people listen to Pink Floyd. 30 people listen to Metallica and 20 people listen to John Denver. If 10 people listen to all three then find the no. of people who listen only Pink Floyd.

Research MethodologyAnswered question

Keegan Stevens 2023-03-21

The volume of a sphere is increasing at a rate of 3 cubic centimetres per second. How fast is the surface area increasing when the radius is 2 centimetres ?

A)$3c{m}^{2}/s$

B)$6c{m}^{2}/s$

C)$12c{m}^{2}/s$

D)$1c{m}^{2}/s$

A)$3c{m}^{2}/s$

B)$6c{m}^{2}/s$

C)$12c{m}^{2}/s$

D)$1c{m}^{2}/s$

Research MethodologyAnswered question

Clinton Mccormick 2023-02-25

Determine the average value of function $y=Asi{n}^{2}x$ in the range x=0 to $x=\pi $.

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presentarab2 2023-02-06

Find the average angular speed of the minute hand of a normal clock in 30 minutes.

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NormmodulxEE 2022-12-03

Find the average value ${f}_{ave}$ of the function f on the given interval.

$f(x)=3{x}^{2}+8x,[-1,2]$

$f(x)=3{x}^{2}+8x,[-1,2]$

Research MethodologyAnswered question

accessedg05 2022-11-28

A negative potential energy is possible. Explain

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Ramiro Wise 2022-11-28

Find the average value fave of the function f on the given interval.

$f(t)=e\mathrm{sin}(t),\mathrm{cos}(t),[0,\frac{\pi}{2}]$

$f(t)=e\mathrm{sin}(t),\mathrm{cos}(t),[0,\frac{\pi}{2}]$

Research MethodologyAnswered question

ra2lokBQ 2022-11-22

On the generalized Sierpinski space

In Sierpiński topology the open sets are linearly ordered by set inclusion, i.e. If $S=\{0,1\}$, then the Sierpiński topology on S is the collection $\{\varphi ,\{1\},\{0,1\}\}$ such that $\varphi \subset \{0\}\subset \{0,1\}$ we can generalize it by defining a topology analogous to Sierpiński topology with nested open sets on any arbitrary non-empty set as follows: Let X be a non-empty set and I a collection of some nested subsets of X indexed by a linearly ordered set $(\mathrm{\Lambda},\le )$ such that I always contains the void set $\varphi $ and the whole set X, i.e.

$I=\{\mathrm{\varnothing},{A}_{\lambda},X:{A}_{\lambda}\subset X,\lambda \in \mathrm{\Lambda}\}$

such that ${A}_{\mu}\subset {A}_{\nu}$ whenever $\mu \le \nu $.

Then it is easy to show that I qualifies as a topology on X.

My questions are:

(1) Is there a name for such a topology in general topology literature?

(2) Is there any research paper studying such type of compact, non-Hausdorff and connected chain topologies?

In Sierpiński topology the open sets are linearly ordered by set inclusion, i.e. If $S=\{0,1\}$, then the Sierpiński topology on S is the collection $\{\varphi ,\{1\},\{0,1\}\}$ such that $\varphi \subset \{0\}\subset \{0,1\}$ we can generalize it by defining a topology analogous to Sierpiński topology with nested open sets on any arbitrary non-empty set as follows: Let X be a non-empty set and I a collection of some nested subsets of X indexed by a linearly ordered set $(\mathrm{\Lambda},\le )$ such that I always contains the void set $\varphi $ and the whole set X, i.e.

$I=\{\mathrm{\varnothing},{A}_{\lambda},X:{A}_{\lambda}\subset X,\lambda \in \mathrm{\Lambda}\}$

such that ${A}_{\mu}\subset {A}_{\nu}$ whenever $\mu \le \nu $.

Then it is easy to show that I qualifies as a topology on X.

My questions are:

(1) Is there a name for such a topology in general topology literature?

(2) Is there any research paper studying such type of compact, non-Hausdorff and connected chain topologies?

Research MethodologyAnswered question

Nico Patterson 2022-11-21

Is the invariant subspace problem open for invertible maps?

Let $T:H\to H$ be a bounded linear operator with bounded inverse on the separable complex Hilbert space. Does T preserve a closed proper non-trival invariant subspace?

I'm aware the question is (famously) open for bounded linear maps, and of partial results, but no survey (or Tao's blog, etc) seem to address the invertible case.

If it is open, does a positive or negative answer imply the answer in the non-invertible case?

Let $T:H\to H$ be a bounded linear operator with bounded inverse on the separable complex Hilbert space. Does T preserve a closed proper non-trival invariant subspace?

I'm aware the question is (famously) open for bounded linear maps, and of partial results, but no survey (or Tao's blog, etc) seem to address the invertible case.

If it is open, does a positive or negative answer imply the answer in the non-invertible case?

Research MethodologyAnswered question

Jaiden Elliott 2022-11-20

Homotopy equivalence between two mapping tori of compositions

For any maps $s:X\to K$ there is defined a homotopy equivalence

$T(d\circ s:X\to X)\to T(s\circ d:K\to K);\phantom{\rule{1em}{0ex}}(x,t)\mapsto (s(x),t).$

Here, T(f) denotes the mapping torus of a self-map $f:Z\to Z$ (not necessarily a homeomorphism). It is very surprising to me that this holds with no extra conditions on d and s. I'm guessing that the homotopy inverse is the map:

$T(s\circ d)\to T(d\circ s),\phantom{\rule{1em}{0ex}}(k,t)\mapsto (d(k),t).$

If the above is a genuine homotopy inverse, then the map:

$(x,t)\mapsto (d(s(x)),t)$

would have to be homotopic to the identity somehow. However, after banging my head against the wall on this for a while I can't come up with a valid homotopy. So my questions are:

Is the map $T(s\circ d)\to T(d\circ s)$ I've defined above actually a homotopy inverse? If so, what is the homotopy from the composition I wrote down above to the identity map?

Is there a better one that makes the homotopy obvious?

For any maps $s:X\to K$ there is defined a homotopy equivalence

$T(d\circ s:X\to X)\to T(s\circ d:K\to K);\phantom{\rule{1em}{0ex}}(x,t)\mapsto (s(x),t).$

Here, T(f) denotes the mapping torus of a self-map $f:Z\to Z$ (not necessarily a homeomorphism). It is very surprising to me that this holds with no extra conditions on d and s. I'm guessing that the homotopy inverse is the map:

$T(s\circ d)\to T(d\circ s),\phantom{\rule{1em}{0ex}}(k,t)\mapsto (d(k),t).$

If the above is a genuine homotopy inverse, then the map:

$(x,t)\mapsto (d(s(x)),t)$

would have to be homotopic to the identity somehow. However, after banging my head against the wall on this for a while I can't come up with a valid homotopy. So my questions are:

Is the map $T(s\circ d)\to T(d\circ s)$ I've defined above actually a homotopy inverse? If so, what is the homotopy from the composition I wrote down above to the identity map?

Is there a better one that makes the homotopy obvious?

Research MethodologyAnswered question

Arendrogfkl 2022-11-20

Finite Math (Probability/Venn Diagram)

13) A survey revealed that 25% of people are entertained by reading books, 39% are entertained by watching TV, and 36% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage.

Is this problem stated correctly? How can 36% of the people be entertained by both books and TV, when only 25% of the people are entertained by reading books?

EDIT

Here are two other questions from the exam, that the instructor said followed the same logic as the question above.

14) Of the coffee makers sold in an appliance store, 5.0% have either a faulty switch or a defective cord, 1.6% have a faulty switch, and 0.2% have both defects. What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage.

15) A survey of senior citizens at a doctor's office shows that 42% take blood pressure-lowering medication, 45% take cholesterol-lowering medication, and 13% take both medications. What is the probability that senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? Express the answer as a percentage.

13) A survey revealed that 25% of people are entertained by reading books, 39% are entertained by watching TV, and 36% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV? Express the answer as a percentage.

Is this problem stated correctly? How can 36% of the people be entertained by both books and TV, when only 25% of the people are entertained by reading books?

EDIT

Here are two other questions from the exam, that the instructor said followed the same logic as the question above.

14) Of the coffee makers sold in an appliance store, 5.0% have either a faulty switch or a defective cord, 1.6% have a faulty switch, and 0.2% have both defects. What is the probability that a coffee maker will have a defective cord? Express the answer as a percentage.

15) A survey of senior citizens at a doctor's office shows that 42% take blood pressure-lowering medication, 45% take cholesterol-lowering medication, and 13% take both medications. What is the probability that senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? Express the answer as a percentage.

Research MethodologyAnswered question

Kayden Mills 2022-11-19

A survey is mailed to a random sample of residents in a city asking whether or not they think the current mayor is doing an acceptable job. What type of bias do you think would most likely be introduced in this type of situation? You can argue for more than one answer but please select the answer that would be the main source of bias. (This question is from your textbook) Group of answer choices

A. Response bias.

The wording of the survey may be confusing or provoke a certain response.

B. Undercoverage.

The entire population is not reached,

C. Nonresponse bias.

People who feel strongly about the mayor are more likely to respond.

A. Response bias.

The wording of the survey may be confusing or provoke a certain response.

B. Undercoverage.

The entire population is not reached,

C. Nonresponse bias.

People who feel strongly about the mayor are more likely to respond.

Research MethodologyAnswered question

Dylan Benitez 2022-11-19

Solve clustering problem. After step $1$ i.e putting each data-point to a cluster now calculate the mean or average of all of the data-points in a specific cluster. let suppose We have some data-points like $A(2,3),B(4,5),C(6,7),D(8,9)$ in a cluster. How can we calculate their average?

Research MethodologyAnswered question

Simone Watts 2022-11-18

Calculate an average or typical time. If I would just use the median (or other "normal" types of calculating an average), for example $23:59$ and $00:01$ would yield $12:00$ when it should $00:00$. Is there a better method?

Research MethodologyAnswered question

Jenny Roberson 2022-11-17

Which of the following is not a form of bias?

Multiple Choice

Those responding to a survey or poll differ systematically from the nonrespondents.

Information from the sample overemphasizes a particular stratum of the population.

Portions of the population are excluded or underrepresented from the sample.

Certain groups in the population are systematically underrepresented in the sample.

Multiple Choice

Those responding to a survey or poll differ systematically from the nonrespondents.

Information from the sample overemphasizes a particular stratum of the population.

Portions of the population are excluded or underrepresented from the sample.

Certain groups in the population are systematically underrepresented in the sample.

Research MethodologyAnswered question

ajumbaretu 2022-11-16

How to identify and distinguish a sample and population mean?

In a village the mean rent was 1830; a rental company comes and surveys with a sample size of 25 for a hypothetical testing to test if the μ is equals 1830 or not.

This new survey gets a mean value of 1700 with a standard deviation of 200.

For the company to deduce t-value(for hypothesis testing) which is sample mean and which will be population mean? I assumed 1830 to be the population mean but it turned out to be the sample mean and 1700 to be the population mean.

In a village the mean rent was 1830; a rental company comes and surveys with a sample size of 25 for a hypothetical testing to test if the μ is equals 1830 or not.

This new survey gets a mean value of 1700 with a standard deviation of 200.

For the company to deduce t-value(for hypothesis testing) which is sample mean and which will be population mean? I assumed 1830 to be the population mean but it turned out to be the sample mean and 1700 to be the population mean.

Research MethodologyAnswered question

anraszbx 2022-11-14

If the average of $1$st $12$ number is $10.8$, average of $1$st 6 number is $10.4$ and the last $6$ number is $11.5$. Find the $6$th number.

Research MethodologyAnswered question

Jared Lowe 2022-11-10

I am self studying, and have the answer to this question at the back of the book. The question is as follows (paraphrase):

A survey of chemical research workers has shown on average that each man requires no cupboard 60% of the time, one cupboard 30% of the time and two cupboards 10% of the time; three or more were never needed. If four chemists work independently, how many cupboards should be provided so that there are adequate facilities at least 95% of the time?

The answer is that 4 cupboards are enough for 95.85% of the time. I just do not know how to get the answer.

A survey of chemical research workers has shown on average that each man requires no cupboard 60% of the time, one cupboard 30% of the time and two cupboards 10% of the time; three or more were never needed. If four chemists work independently, how many cupboards should be provided so that there are adequate facilities at least 95% of the time?

The answer is that 4 cupboards are enough for 95.85% of the time. I just do not know how to get the answer.

Research MethodologyAnswered question

Abdiel Mays 2022-11-09

A survey is conducted and 3 people are to be chosen from a group of 20.

a) In how many different ways could the 3 be chosen? (1140)

b) If a group contains 8 men and 12 women, how many groups containing exactly 1 man are possible? (528)

A solution for question b) is wanted. How can I solve this problem?

a) In how many different ways could the 3 be chosen? (1140)

b) If a group contains 8 men and 12 women, how many groups containing exactly 1 man are possible? (528)

A solution for question b) is wanted. How can I solve this problem?

In any research, the researcher uses some kind of methodology to guide them in their work. The methodology is the set of principles and procedures followed by the researcher in order to arrive at the conclusions of their research. There are different types of research methodology, and each has its advantages and disadvantages. The most common types of research methodology are: surveys, experiments, observation, and case studies. The choice of research methodology depends on the nature of the research question and the goals of the researcher. For example, if the researcher wants to study a phenomenon in its natural setting, they would use an observational methodology. If the researcher wants to test a hypothesis, they would use an experimental methodology.