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Explanation & Answer
(−4, -2) and has a slope of 5
y1 = - 2 x1 = - 4 c = 18 m = 5
y - y1 = m(x - x1)
y + 2 = 5(x + 4)
y + 2 = 5x + 20
5x - y + 18 = 0
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Vila Health ® ActivityPresenting Statistical Results for Decision MakingIntroductionYour OfficeStakeholder InterviewsEmail ResponseConclusionIntroductionAt any enterprise, statistical results can point the way to better decisions. This is especially true in health care, where trends or changes in patient care or results can have powerful effects on health care organizations — clinical effects, and financial effects. Knowing the facts about trends and changes is crucial to navigating them, which means that in many ways, statistical results are powerful tools.But they’re less powerful if nobody understands them. More often than not, stakeholders in health care organizations are not well versed in statistics or data analysis. Especially for these stakeholders, it’s critical to make careful choices about which numbers to include — and how to talk about those numbers. Doing so helps you to present statistical results in a way that’s understandable and actionable even for those with less data literacy.In this activity, you’ll have an opportunity to analyze a health trend at a large urban hospital, and to decide which results of the analysis are most important to communicate to the stakeholders concerned with it.Your OfficeYou are an analyst in the Quality Assurance department at St. Anthony Medical Center, a large hospital in Minneapolis, Minnesota. You have an email from David Brooks, the manager of Quality Assurance, in which he explains your next assignment.EmailFrom: David BrooksSubject: HACsHello! So I’m aware that you’re relatively new around here, but I’ve got to pull you in on an important project. Here’s the short version, and I can answer questions later if this isn’t enough background.Since you’re in health care, you must know that hospital-acquired conditions (HACs) are a big deal. Hospitals are designed from the ground up to minimize them, but the fact is that hospitals always have a lot of bugs floating around and that means they’re a constant danger. And while we try to minimize mistakes, health care professionals are human, and sometimes mistakes cause real problems.The hospital’s board is getting worked up about them again, because we’ve had some high-profile cases where a patient went home and had to be readmitted because of a mistake or an infection they picked up while they were here. They’re worried about PR, of course, but they’re worried about patient outcomes, and — of course — financial reimbursement and penalties, too.What I need you to do is start working on a presentation about HACs here, specifically as they relate to staffing levels and skill mix. That presentation should explain our recommendations to the board. You’ll want to include some statistics to bolster our case, so take a look at the AHRQ National Scorecard on Hospital-Acquired Conditions and the CMS Hospital-Acquired Conditions Reduction Program. Look at published research about the relationship between HACs and staffing levels, too.Let’s get this right; this is our chance to get the board to understand that HACs will go down if they do what we recommend.Go talk to Rick Susskind first; he’s our senior data analyst and he’s already been working on this. He has completed a data analysis on this, and he can explain what the variables are. You’ll have to talk to a few other people too, to get everything you need.DavidEmailFrom: Rick SuskindSubject: HAC DataHi! I got your message about the HAC question. I’ve attached a spreadsheet of the data analysis we’ve got on that.Here are a few variables that might be unclear:HAC_Rate: That’s the number of HACs per 1,000 discharges. You could say it’s the measure for the extent of hospital errors.Nursing_HPPD: That’s the number of nursing staff hours per patient day. It’s the hospital’s nurse staffing level.Skill_Mix: That’s obviously about skill mix, but specifically, it’s the percentage of nursing staff hours that are provided by registered nurses, as opposed to other professionals.ALOS: That stands for average length of stay; it’s the number of inpatient days per hospital discharge. It’s a measure of how efficient the hospital is.Let me know if you have other questions! Oh, you’ll need to find out how many discharges we have per year. I don’t know that, but Troy Holland, our vice president of patient services, will know.Attachment: HAC AnalysisStakeholder InterviewsTroy HollandVice President of Patient ServicesIt’s nice to meet you! Yep, I’ve got those discharge stats. I’m assuming you’re confining your analysis to the last full year? If so, the number of discharges for last year was 10,000. That includes both adult and pediatric discharges.What I don’t have is information about nurse staffing or costs. For those, you’ll want to talk to Jackie, the chief nursing officer.Jackie SandovalChief Nursing OfficerHello. I understand you need some data about our staff costs related to nursing. I’ve got three numbers for you.Our cost per nurse is $72,000. Now, that’s an average of nurses and registered nurses.Our cost per registered nurse is $85,000.Per licensed practical nurse, it’s $52,000. Those numbers include salary, benefits, and overhead.You had asked about some other costs, but I don’t have those. You’ll want to talk to the CFO, Owen Welch.Owen WelchChief Financial OfficerHey, I’ve only got a couple of minutes but here’s what you asked about: Our cost per inpatient day is $2,600, and the penalty per HAC is $5,700.Email ResponseIt looks like David has followed up with you about the data analysis project you’re working on. Review David's latest message to you and send a reply with your initial thoughts.EmailFrom: David BrooksSubject: HACsThanks for doing all that running around. Now that you’ve got the data analysis you need, I’d like you to do some thinking about what results you’re going to include in the presentation. Remember, it’s the board, not a bunch of number geeks. You’ll want to give them the statistical results they need to make a decision, not just every bit of data we have.Write down a list of numbers you’re thinking about including in your presentation. We really need to make a data-driven recommendation to the board, and I’d really appreciate your expertise. Thanks!ReplySubject: RE: HACsThis message has not been composed yet.ConclusionIn this activity, you saw that while complicated analysis of data is an important step in guiding decisions at health care organizations, it’s not the only step. Decision makers need to understand how the data were collected, how variables are measured, and whether the analysis tools and techniques were appropriate.You also gathered necessary data for an analysis of HACs, nurse staffing levels, and skill mix, and did some pre-work on a presentation of the data analysis to the hospital’s board.
22 pages
Part 2
An analyst at a local bank wonders if the age distribution of customers coming for service at his branch 1 What is the nu ...
Part 2
An analyst at a local bank wonders if the age distribution of customers coming for service at his branch 1 What is the null hypothesis if you want to ...
please double check and correct this (if need be!)
1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state yo ...
please double check and correct this (if need be!)
1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state your solution as an ordered pair.1. The first thing I did was put both equations in the form of
y=mx+b. That way it makes them easy to graph and I will know the slope (m) and
the y intercept (b) of each.
The first equation is already in y=mx+b.
y=1/2x + 5/2 means the slope of this line is m=1/2 and the y
intercept is 5/2.
For the second equation I moved numbers around.
It started off as 3x+2y=1.
First I subtracted 3x from both sides to get 2y=-3x+1.
Next I divided 2 to every term in the equation to get y alone.
You get y=-3/2x+1/2.
Now that this is in y=mx+b form, I know that the slope of this
line is m=-3/2 and the y intercept is 1/2.
Knowing this information it can now be graphed.
I first graphed the line with the slope of 1/2 and y intercept
of 5/2.
The line intercepts the y-axis at 5/2 so there should have a dot
at 5/2 or 2.5
Now from there we need a second point to make the line.
If the slope is 1/2 that means we can either go from this point
UP 2 and RIGHT 1 or DOWN 2 and LEFT 1 and can keep doing this from every point.
Next, I did the same thing for the line where slope is -3/2 (or
-1.5) and has a y intercept of 1/2.
I drew the y intercept first on the y line at the 1/2 point
between 0 and 1.
Since it is a negative slope this time we go either DOWN 2 and
RIGHT 3 or UP 2 and LEFT 3 from each point.
The lines both meet up at the point (-1, 2) so
this is the answer!
Solving algebraically:
I set the two equations equal to each other by substituting one
of the variables.
I have y=1/2x+5/2 and y=-3/2x+1/2.
If y equals that, you can replace y with the thing y equals in
the other equation.
You should get 1/2x+5/2=-3/2x+1/2.
Add 3/2x to both sides and you get 4/2x+5/2=1/2.
Then subtract 5/2 from both sides to get 4/2x=-4/2.
Simplify 4/2 by dividing and you get 2x=-2.
Finally, divide by 2 to both sides and you get x=-1.
Now to get the y variable plug x=-1 back into EITHER equation by
replacing wherever it says x with a -1.
I chose to plug in to y=1/2(-1)+5/2.
Multiplying you get y=-1/2+5/2.
Adding you get y=4/2. Dividing that you get y=2.
Then the answer again is in the form of (x,y) so the answer is (-1,
2) It is the same answer both ways.
2. The population of a country is initially 2.5 million people and is increasing by 0.8 million people every year. The country’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate for an additional 0.4 million people per year.a. Based on these assumptions, in approximately how many years will the country first experience shortages of food?b. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.c. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.2.a). I used the
variable ‘x’ in place of the unknown years:
Current
population is 2.5+0.8x where x is 0
Currently
supply is 4+0.4x where x= 0
2.5+0.8x=4+0.4x
0.8x-0.4x=4-2.5
0.4x=1.5
X=1.5/0.4
=3.75
X=3.75
years is when supply will be equal to the demand of the population
Therefore,
the above 3.75 years there will be shortage of food.
Rounding
off to the next year we have X=4 years this indicates the years that food
shortage will be experienced.
The answer is approximately 4 years.
b. Initial food supply is 4 million
4x2=8
Supply
function
8+0.5x
Using
population function
2.5+0.8x
8+0.5x=2.5+0.8x
0.5x-0.8x=2.5-8
-0.3x=-5.5
X=5.5/0.3
X=18.3333
years
X=18.3333
years this is actually the time supply will be equal to the demand of the
population
Therefore
above 18.3333 years there will be shortage.
Hence 19 years to come it means that there will be
food shortage
c. Supply function 2(4+0.4x) =8+0.8x
Population
function is 2.5+0.8x
Therefore
8+0.8x=2.5+0.8x
0.8x-0.8x=2.5-8
0=-5.5 and this is a false statement
This means that for the rest of the years food will
be adequate.
The negative (-) 5.5 means that each year will have
an additional food for 5.5 million people although it does not increase.
3. Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 500 and 600 (inclusive), the number of upperclassmen (11th and 12th graders) must fall between 400 and 500 (inclusive), and the number of students cannot exceed 1000.a. Let x represent the number of underclassmen and y represent the number of upperclassmen. Write a system of inequalities that models the situation.b. Graph the solution to the system of inequalities in part a.3. For this one I graphed the equation on a number line. I made
underclassmen x and upperclassmen y.
The number of underclassmen has to fall between 500 and 600 and
inclusive means that it can actually equal 500 or 600. Represent this
with 500</=x</=600
Upperclassmen have to be between 400 and 500. Represent this
with 400</=y</=500
It also says the total number of students cannot exceed 1000
which means they have to be less than or equal to 1000.
Represent this with the underclassmen plus the upperclassmen is
less than or equal to 1000 or in equation form x+y</=1000
The three equations should be:
500</=x</=600
400</=y</=500
x+y</=1000
If you know the minimum x can be is 500 and the minimum y can be
is 400 then you know the minimum number of students in the school can be 900. x
and y together could also get as high as 1100 but it tells you that
upperclassmen and underclassmen together cannot exceed 1000. That means the
number of students in the school must be greater than or equal to 900 and less
than or equal to 1000.
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MHA-FP5017 Assignment 4- Presenting Statistical Results for Decision Making
Vila Health ® ActivityPresenting Statistical Results for Decision MakingIntroductionYour OfficeStakeholder InterviewsEmail ResponseConclusionIntroductionAt any enterprise, statistical results can point the way to better decisions. This is especially true in health care, where trends or changes in patient care or results can have powerful effects on health care organizations — clinical effects, and financial effects. Knowing the facts about trends and changes is crucial to navigating them, which means that in many ways, statistical results are powerful tools.But they’re less powerful if nobody understands them. More often than not, stakeholders in health care organizations are not well versed in statistics or data analysis. Especially for these stakeholders, it’s critical to make careful choices about which numbers to include — and how to talk about those numbers. Doing so helps you to present statistical results in a way that’s understandable and actionable even for those with less data literacy.In this activity, you’ll have an opportunity to analyze a health trend at a large urban hospital, and to decide which results of the analysis are most important to communicate to the stakeholders concerned with it.Your OfficeYou are an analyst in the Quality Assurance department at St. Anthony Medical Center, a large hospital in Minneapolis, Minnesota. You have an email from David Brooks, the manager of Quality Assurance, in which he explains your next assignment.EmailFrom: David BrooksSubject: HACsHello! So I’m aware that you’re relatively new around here, but I’ve got to pull you in on an important project. Here’s the short version, and I can answer questions later if this isn’t enough background.Since you’re in health care, you must know that hospital-acquired conditions (HACs) are a big deal. Hospitals are designed from the ground up to minimize them, but the fact is that hospitals always have a lot of bugs floating around and that means they’re a constant danger. And while we try to minimize mistakes, health care professionals are human, and sometimes mistakes cause real problems.The hospital’s board is getting worked up about them again, because we’ve had some high-profile cases where a patient went home and had to be readmitted because of a mistake or an infection they picked up while they were here. They’re worried about PR, of course, but they’re worried about patient outcomes, and — of course — financial reimbursement and penalties, too.What I need you to do is start working on a presentation about HACs here, specifically as they relate to staffing levels and skill mix. That presentation should explain our recommendations to the board. You’ll want to include some statistics to bolster our case, so take a look at the AHRQ National Scorecard on Hospital-Acquired Conditions and the CMS Hospital-Acquired Conditions Reduction Program. Look at published research about the relationship between HACs and staffing levels, too.Let’s get this right; this is our chance to get the board to understand that HACs will go down if they do what we recommend.Go talk to Rick Susskind first; he’s our senior data analyst and he’s already been working on this. He has completed a data analysis on this, and he can explain what the variables are. You’ll have to talk to a few other people too, to get everything you need.DavidEmailFrom: Rick SuskindSubject: HAC DataHi! I got your message about the HAC question. I’ve attached a spreadsheet of the data analysis we’ve got on that.Here are a few variables that might be unclear:HAC_Rate: That’s the number of HACs per 1,000 discharges. You could say it’s the measure for the extent of hospital errors.Nursing_HPPD: That’s the number of nursing staff hours per patient day. It’s the hospital’s nurse staffing level.Skill_Mix: That’s obviously about skill mix, but specifically, it’s the percentage of nursing staff hours that are provided by registered nurses, as opposed to other professionals.ALOS: That stands for average length of stay; it’s the number of inpatient days per hospital discharge. It’s a measure of how efficient the hospital is.Let me know if you have other questions! Oh, you’ll need to find out how many discharges we have per year. I don’t know that, but Troy Holland, our vice president of patient services, will know.Attachment: HAC AnalysisStakeholder InterviewsTroy HollandVice President of Patient ServicesIt’s nice to meet you! Yep, I’ve got those discharge stats. I’m assuming you’re confining your analysis to the last full year? If so, the number of discharges for last year was 10,000. That includes both adult and pediatric discharges.What I don’t have is information about nurse staffing or costs. For those, you’ll want to talk to Jackie, the chief nursing officer.Jackie SandovalChief Nursing OfficerHello. I understand you need some data about our staff costs related to nursing. I’ve got three numbers for you.Our cost per nurse is $72,000. Now, that’s an average of nurses and registered nurses.Our cost per registered nurse is $85,000.Per licensed practical nurse, it’s $52,000. Those numbers include salary, benefits, and overhead.You had asked about some other costs, but I don’t have those. You’ll want to talk to the CFO, Owen Welch.Owen WelchChief Financial OfficerHey, I’ve only got a couple of minutes but here’s what you asked about: Our cost per inpatient day is $2,600, and the penalty per HAC is $5,700.Email ResponseIt looks like David has followed up with you about the data analysis project you’re working on. Review David's latest message to you and send a reply with your initial thoughts.EmailFrom: David BrooksSubject: HACsThanks for doing all that running around. Now that you’ve got the data analysis you need, I’d like you to do some thinking about what results you’re going to include in the presentation. Remember, it’s the board, not a bunch of number geeks. You’ll want to give them the statistical results they need to make a decision, not just every bit of data we have.Write down a list of numbers you’re thinking about including in your presentation. We really need to make a data-driven recommendation to the board, and I’d really appreciate your expertise. Thanks!ReplySubject: RE: HACsThis message has not been composed yet.ConclusionIn this activity, you saw that while complicated analysis of data is an important step in guiding decisions at health care organizations, it’s not the only step. Decision makers need to understand how the data were collected, how variables are measured, and whether the analysis tools and techniques were appropriate.You also gathered necessary data for an analysis of HACs, nurse staffing levels, and skill mix, and did some pre-work on a presentation of the data analysis to the hospital’s board.
22 pages
Part 2
An analyst at a local bank wonders if the age distribution of customers coming for service at his branch 1 What is the nu ...
Part 2
An analyst at a local bank wonders if the age distribution of customers coming for service at his branch 1 What is the null hypothesis if you want to ...
please double check and correct this (if need be!)
1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state yo ...
please double check and correct this (if need be!)
1. Solve the system of equations below both algebraically and by graphing. Be sure to show all of your work and state your solution as an ordered pair.1. The first thing I did was put both equations in the form of
y=mx+b. That way it makes them easy to graph and I will know the slope (m) and
the y intercept (b) of each.
The first equation is already in y=mx+b.
y=1/2x + 5/2 means the slope of this line is m=1/2 and the y
intercept is 5/2.
For the second equation I moved numbers around.
It started off as 3x+2y=1.
First I subtracted 3x from both sides to get 2y=-3x+1.
Next I divided 2 to every term in the equation to get y alone.
You get y=-3/2x+1/2.
Now that this is in y=mx+b form, I know that the slope of this
line is m=-3/2 and the y intercept is 1/2.
Knowing this information it can now be graphed.
I first graphed the line with the slope of 1/2 and y intercept
of 5/2.
The line intercepts the y-axis at 5/2 so there should have a dot
at 5/2 or 2.5
Now from there we need a second point to make the line.
If the slope is 1/2 that means we can either go from this point
UP 2 and RIGHT 1 or DOWN 2 and LEFT 1 and can keep doing this from every point.
Next, I did the same thing for the line where slope is -3/2 (or
-1.5) and has a y intercept of 1/2.
I drew the y intercept first on the y line at the 1/2 point
between 0 and 1.
Since it is a negative slope this time we go either DOWN 2 and
RIGHT 3 or UP 2 and LEFT 3 from each point.
The lines both meet up at the point (-1, 2) so
this is the answer!
Solving algebraically:
I set the two equations equal to each other by substituting one
of the variables.
I have y=1/2x+5/2 and y=-3/2x+1/2.
If y equals that, you can replace y with the thing y equals in
the other equation.
You should get 1/2x+5/2=-3/2x+1/2.
Add 3/2x to both sides and you get 4/2x+5/2=1/2.
Then subtract 5/2 from both sides to get 4/2x=-4/2.
Simplify 4/2 by dividing and you get 2x=-2.
Finally, divide by 2 to both sides and you get x=-1.
Now to get the y variable plug x=-1 back into EITHER equation by
replacing wherever it says x with a -1.
I chose to plug in to y=1/2(-1)+5/2.
Multiplying you get y=-1/2+5/2.
Adding you get y=4/2. Dividing that you get y=2.
Then the answer again is in the form of (x,y) so the answer is (-1,
2) It is the same answer both ways.
2. The population of a country is initially 2.5 million people and is increasing by 0.8 million people every year. The country’s annual food supply is initially adequate for 4 million people and is increasing at a constant rate for an additional 0.4 million people per year.a. Based on these assumptions, in approximately how many years will the country first experience shortages of food?b. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.c. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? If so, how many years would it take for shortages to occur? If not, explain.2.a). I used the
variable ‘x’ in place of the unknown years:
Current
population is 2.5+0.8x where x is 0
Currently
supply is 4+0.4x where x= 0
2.5+0.8x=4+0.4x
0.8x-0.4x=4-2.5
0.4x=1.5
X=1.5/0.4
=3.75
X=3.75
years is when supply will be equal to the demand of the population
Therefore,
the above 3.75 years there will be shortage of food.
Rounding
off to the next year we have X=4 years this indicates the years that food
shortage will be experienced.
The answer is approximately 4 years.
b. Initial food supply is 4 million
4x2=8
Supply
function
8+0.5x
Using
population function
2.5+0.8x
8+0.5x=2.5+0.8x
0.5x-0.8x=2.5-8
-0.3x=-5.5
X=5.5/0.3
X=18.3333
years
X=18.3333
years this is actually the time supply will be equal to the demand of the
population
Therefore
above 18.3333 years there will be shortage.
Hence 19 years to come it means that there will be
food shortage
c. Supply function 2(4+0.4x) =8+0.8x
Population
function is 2.5+0.8x
Therefore
8+0.8x=2.5+0.8x
0.8x-0.8x=2.5-8
0=-5.5 and this is a false statement
This means that for the rest of the years food will
be adequate.
The negative (-) 5.5 means that each year will have
an additional food for 5.5 million people although it does not increase.
3. Springfield will be opening a new high school in the fall. The number of underclassmen (9th and 10th graders) must fall between 500 and 600 (inclusive), the number of upperclassmen (11th and 12th graders) must fall between 400 and 500 (inclusive), and the number of students cannot exceed 1000.a. Let x represent the number of underclassmen and y represent the number of upperclassmen. Write a system of inequalities that models the situation.b. Graph the solution to the system of inequalities in part a.3. For this one I graphed the equation on a number line. I made
underclassmen x and upperclassmen y.
The number of underclassmen has to fall between 500 and 600 and
inclusive means that it can actually equal 500 or 600. Represent this
with 500</=x</=600
Upperclassmen have to be between 400 and 500. Represent this
with 400</=y</=500
It also says the total number of students cannot exceed 1000
which means they have to be less than or equal to 1000.
Represent this with the underclassmen plus the upperclassmen is
less than or equal to 1000 or in equation form x+y</=1000
The three equations should be:
500</=x</=600
400</=y</=500
x+y</=1000
If you know the minimum x can be is 500 and the minimum y can be
is 400 then you know the minimum number of students in the school can be 900. x
and y together could also get as high as 1100 but it tells you that
upperclassmen and underclassmen together cannot exceed 1000. That means the
number of students in the school must be greater than or equal to 900 and less
than or equal to 1000.
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