Capella Age of Children Accessing Services Frequency Distribution Paper SPSS: Frequency Statistics
ASSIGNMENT OVERVIEW
By successfully completing this assignment, you demonstrate your proficiency in the following competency and specialized behaviors:
Competency 4: Engage in practice-informed research and research-informed practice.
C4.SP.A: Apply leadership skills, decision making, and the use of technology to inform evidence-based research practice to develop, implement, evaluate, and communicate interventions across the specialization of advanced generalist practice settings.
Related Assignment Criteria:
1: Devise accurate SPSS datasets.
3: Describe and report the statistical method or test outcomes using the appropriate statistical method or test.
C4.SP.B: Apply leadership skills, decision making, and the use of technology to inform program evaluation to develop, implement, evaluate, and communicate interventions across the specialization of advanced generalist practice settings.
Related Assignment Criteria:​
2: Develop appropriate statistical tests and reports that assist in program evaluation.
4: Apply critical thinking in verbal and written communication through the use of leadership and technology.
ASSIGNMENT SCENARIO
You are evaluating the mental health services provided to children by your agency. The agency provides trauma-informed counseling services to children and youth, ages 5–18. The agency’s goal is to have a relatively equal distribution of children and youth, in terms of ages, who seek services.
You will complete a frequency distribution of the number and ages of children who accessed services within your community agency over the past month. You will need to provide a histogram and summary of your analysis. Consider the implications of the findings as you plan for next year’s programming.
Also refer to the tutorial provided in the first study in this unit as a reference on how to conduct frequency distributions.
ASSIGNMENT INSTRUCTIONS
Using the Unit 2 Dataset 2 given in the resources, respond to the following prompts:
Create an SPSS file that includes the ages and number of children who have accessed services to your agency over the past year. The SPSS output, which can be copied and pasted into a Word document, should include a chart showing the frequency statistics.
Develop a histogram to demonstrate the number of children and their ages.
Consider that the main goal for using frequency distribution is to simplify large datasets. Graphs provide us with a tool to interpret the data. Addressing the prompts below, provide a brief narrative summary that you would provide to the Ray Foundation to describe the age of children and frequency of services used.
Interpret the data displayed in the SPSS output graphs you created.
What trends do you see in the usage of mental health services?
How do these trends affect your planning for the program?
What would be your next steps if you wanted to see a representation of all age groups at your agency?
ADDITIONAL REQUIREMENTS
Your assignment should meet the following requirements:
Written communication: Written communication is free of errors that detract from the overall message.
APA formatting: Resources and citations are formatted according to current APA style and formatting standards.
Length of paper: One double-spaced page.
Font and font size: Times New Roman, 12 point Contents
Introduction
2
How to Write the Lab Report
5
Measurements and Uncertainties
7
Basic Electricity and Magnetism
11
Electric Fields and Equipotential Lines
15
Deflection of Electrons in an Electric Field
19
Ohm’s Law
23
Resistors in Series and Parallel
25
The Potentiometer
27
Determination of an Unknown Resistance Using a Wheatstone Bridge
31
Charging and Discharging of a Capacitor
35
Magnetic Field Around a Wire
37
Magnetic Field of Solenoid
39
Faraday’s Law
41
Rays, Mirrors, and Thin Lenses
43
Diffraction of Light
47
Appendix A – Resistor Color Coding
49
Appendix B – The Breadboard
51
Appendix C – Uncertainty and Error Propagation
53
2014 Revisions: Nayeli Zuniga-Hansen, Ali Abu-Nada, Robert Baer, Richard West
1
Introduction
The purpose of the introductory physics laboratory is to give students the opportunity to
examine, firsthand, some of the concepts and laws of physics.
Physics is an accessible, tangible science. Physical phenomena are all around us at all
times, so much so that we often take the laws of physics for granted. In this lab you are asked to
examine more closely some natural phenomena and the laws that govern them. Physics is more
than abstract concepts and mathematical formulas; it is a dynamic, living field of study, which is
built upon information gathered from centuries of careful study and consideration of the
universe. The laws of physics are applicable to everything from the very large – planets, stars,
galaxies – to the very small – molecules, atoms, protons, and electrons. This course will show you
how scientists explore the physical laws of the universe.
The first step in our inquiry of the universe is to observe a physical entity or process. The
next step is to compare our observation with existing knowledge to see if the observation
conforms to our present understanding. If it does not then both theorists and experimentalists
examine the problem further. The theorist examines known information and then constructs a
model or theory within which the observation may be explained. The experimentalist gathers
further information to aid the theorist and also tests the predictions made by the theory. This
process may continue for decades as scientific knowledge is accumulated.
Most students who take introductory physics courses do not become scientists. However,
the principles, information, and techniques may be taken with them into any career. We live in
an increasingly technological society; as citizens we are being asked to make decisions which
will not only affect our lives, but the lives of many generations to come. A solid background in
scientific principles and an understanding of the way in which science is conducted will assist
you in making these difficult decisions.
Your objectives in this lab are as follows:
gain hands-on experience and firsthand knowledge of physical principles
acquire training in the scientific method including techniques of accurate observation
and the recording and handling of data
improve logical and rational thinking skills
acquire laboratory techniques including the operation and adjustment of specialized
equipment
understand the limitations and uncertainties inherent in scientific measurements
learn how to gather, organize, and analyze data to determine valid physical
relationships
learn how to present experimental conditions, observations, results and conclusions
Laboratory Instructions
Prior to each experiment, you should prepare as follows:
Read the entire experimental procedure as given in this manual.
Review the corresponding material in your text to gain a further understanding of the
physical concepts to be tested.
Prepare a “Prelab” as described on the next page.
2
Enter the lab with an understanding of the experiment and the procedure
The lab period is organized as follows:
1. The instructor will collect the Prelabs.
2. Students will go to a workstation and if necessary, make further preparations before the
class begins.
3. The instructor will discuss the experiment briefly and demonstrate the equipment.
Take note of any information the instructor may give that is not included in this manual,
especially precautions with regard to the proper handling of equipment. Some
apparatuses are especially fragile and easy damaged.
4. Students will then break into the smallest groups possible, usually two people, to carry
out the experiment. Cooperate with your partner(s) in such a way that each person has the
opportunity to use the experimental equipment. Work as quietly as possible so that others
may concentrate on their experiments.
5. Some equipment must be checked out from the instructor. One person from each group
will exchange a student ID card (or other appropriate ID) for the equipment. At the end of
the experiment the ID will be exchanged for the equipment.
6. Be honest in making and recording observations. Record data as it is indicated by the
equipment. If the results seem to be outside the limits of what is expected, recheck the
equipment and your calculations. If the result is still not what was expected, make the
best possible determination of the sources of error to explain the discrepancy.
7. At the end of the experiment, your work area must be cleaned and organized.
After the lab has been completed, prepare your Lab Report as described below. This report
should contain only your own work. Copy no data, calculations, or conclusions from any source
other than your own work.
Report Formats
The Prelab
This report is due at the beginning of the lab period. This report will count for a grade
and failure to submit can result in a zero grade for the experiment. After having studied this
manual and developed an understanding of the theory and procedure of the experiment, you will
prepare a one page report which will include the following: the title, your name, the object or
purpose of the experiment in your own words, a listing of the equipment you expect to use, a
paraphrased procedure, and a short (usually two or three sentences) description of the theory
behind the experiment.
The Lab Report
This report will be submitted after the experiment has been completed and will be due on
a date which will be specified by your instructor.
The final lab report includes:
1. Title Section: title, your partner’s name, and the date the experiment was performed
3
2. Apparatus: a listing of the equipment which was actually used
3. Introduction: includes the theory and purpose of the experiment
4. Results: includes data sheets, calculations, data tables, and graphs
5. Error Analysis: includes error calculations and a discussion of the specific sources of
error
6. Discussion and Conclusion
7. Answers to Questions
The sections numbered 4, 5, 6 and 7 above are the most important sections of the report as they
demonstrate to your instructor your level of understanding of the experiment and these will be
weighed heavily in determining you grade. In section 5, error analysis, you will discuss the ways
in which the experimental results deviated from what had been predicted by theory. In the
discussion and conclusion section a serious statement is made about what was determined in the
experiment, the ways in which the experiment might be improved, and whether or not the tested
theory has been shown to be valid. At the end of the report all questions listed in the lab manual
and added by your instructor must be answered.
4
How to Write the Lab Report – Sample Instruction
Experimental Investigation of π
A sample lab report for this activity is provided below as an example for you to follow
when writing future lab reports.
Apparatus
Ruler, Vernier caliper, penny, marble, “D” cell, PVC cylinders.
Introduction
How is the circumference of a circle related to its diameter? In this lab, you design an
experiment to test a hypothesis about the geometry of circles. This activity is an introduction to
physics laboratory investigations. It is designed to give practice taking measurements, analyzing
data, and drawing inferences without requiring any special knowledge about physics.
Five objects were chosen such that measurements of their circumference and diameter
could be obtained easily and would be reproducible. Therefore, we did not use irregularly shaped
objects or ones that could be deformed when measured. The diameter of each of the five objects
was measured with either the ruler or caliper. The circumference and diameter of each object was
measured with the same measuring device in case the two instruments were not calibrated the
same. The circumference measurement was obtained by tightly wrapping a small piece of paper
around the object, marking the circumference on the paper with a pencil, and measuring this
distance with the ruler or caliper. The uncertainty specified with each measurement is based on
the precision of the measuring device and the experimenter’s estimated ability to make a reliable
measurement.
Results
The C/D value for the penny is (5.93 cm) / (1.90 cm) = 3.12 (no units). Results for all
five objects are given in the Table 1.
Table 1.
Object
Description
Diameter
± uncertainty
(mm)
Circumference
± uncertainty
(mm)
=C/D
(-)2
Penny
19.0±0.05
59.3±0.5
3.12
0.0004
“D” cell battery
33.0±0.05
104.5±0.5
3.17
0.0009
PVC cylinder A
42.3±0.05
133.0±0.5
3.14
0.00
PVC cylinder B
60.4±0.05
184.5±0.5
3.06
0.0064
Tomato soup can
66.0±0.05
212.0±0.5
3.21
0.0049
= 3.14
(-)2 = 0.0126
5
Error Analysis
The uncertainty of the instrument is ± ½ the smallest increment of measurement. If the
circumference is proportional to the diameter, we should get a straight line through the origin.
From our numerical results, we would expect the slope of the C vs. D graph to be equal to π. The
slope of the best fit line is 3.15, which is equal to π within its uncertainty. The R squared statistic
shows that the data all fall very close to the best fit line. If all the data lie exactly on the fitted
line, R squared is equal to 1. If the data are randomly scattered, R squared is zero. With an R 2
value of 0.997, our linear equation appears to fit the data very well.
Discussion and Conclusions
Our results support the original hypothesis for 5 circles ranging in size from 20 mm to 70
mm in diameter. The C/D ratio for our objects is essentially constant (3.14 ± 0.056) and equal to
π. The specified uncertainty is the standard deviation of the C/D ratio for the five objects.
Graphical analysis also supports the “directly proportional” hypothesis. The line has an intercept
(-0.5 ± 0.5) that is equal to zero within the uncertainty and a slope 3.15 equal to π within error. A
more extensive investigation of this C/D relationship over a wider range of circle sizes should be
performed to verify that this ratio is indeed constant for all circles.
Questions
1)
=[0.0126/(5-1)]1/2 = [0.00315]1/2 = 0.056
So, = 3.14 0.056
2) Plot the relation between c and d.
250
C = 3.15D – 0.502
Circumference
200
150
100
50
0
0
10
20
30
40
50
60
70
Diameter
C
−
3) The slope = D= 2 − 1 = 3.15.
2
1
4) The slope represents the numerical value of
−
5) Percentage error = |
3.142 − 3.14
=|
3.142
| ×100%
| = 0.064 %
6
Experiment 1
Measurements and Uncertainties
Apparatus
Ruler, Vernier caliper, paper strip (or paper tape), five wooden discs of varying diameters
Introduction
Measurement
A measurement tells us about a property of something. It might tell us how heavy an
object is, or how hot it is, or how long it is. A measurement gives a number to that property.
Measurements are always made using an instrument of some kind. Rulers, stopwatches,
weighing scales, and thermometers are all measuring instruments. The result of a measurement is
normally in two parts: a number and a unit of measurement, e.g. ‘How long is it? … 2 meters.’
Uncertainty of measurement
In an ideal world, measurements are always perfect: wooden boards can be cut to exactly
two meters in length and a known volume of steel will have a mass of exactly three kilograms.
However, we live in the real world and measurements are not perfect. In our world, measuring
devices have limitations. The imperfection inherent in all measurements is called an uncertainty.
In this laboratory, we will encounter uncertainty almost every time we make a measurement. Our
notation for measurements and their uncertainties takes the following form:
(Measured value ± Uncertainty) proper units
where the ± is read as “plus or minus”.
9.801 m/s2
9.794
9.796
9.798
9.800
9.802
9.804
9.806
Figure 1.1. Measurement and uncertainty: 9.801 ± 0.003 m/s2
Consider an acceleration due to gravity measurement, g = 9.801 ± 0.003 m/s2. We
interpret this measurement as meaning that the experimentally determined value of g can lie
anywhere between the values 9.801 + 0.003 m/s2 and 9.801 – 0.003 m/s2, or 9.798 m/s2 ≤ g ≤
9.804 m/s2. As you can see, a real world measurement is not merely one simple measured value,
but is actually a range of possible values (see Figure 1.1). This range is determined by the
uncertainty in the measurement. As uncertainty is reduced, this range is narrowed.
7
Sometimes we want to talk about measurements more generally, and so we write them
without actual numbers.
(X± ∆X)
and
(Y ± ∆Y)
In the laboratory, you will not only be taking measurements, but also comparing them.
You will compare your experimental measurements (i.e. the ones you find in lab) to some
theoretical, predicted, or standard measurements as well as to experimental measurements you
make during a second (or third) data run. We need a method to determine how closely these
measurements compare.
Standard deviation
Let’s say we wanted to calculate the standard deviation for the amounts of gold coins
pirates on a pirate ship have. There are 5 pirates on the ship. In statistical terms this means we
have a population of 5 (N=5). If we know the amount of gold coins each of the 5 pirates have, we
use the standard deviation equation for a sample of population:
where, s = the standard deviation.
= each value in the population.
̅ = the mean (average) of the values.
N= the number of values (the population)
In the case where we have a sample size of 5 pirates, we will be using the standard
deviation equation for a sample of a population. Here are the amounts of gold coins the 5 pirates
have:
x1=4, x2=2, x3=5, x4=8, x5=6.
Now, let’s calculate the standard deviation:
1. Calculate the mean:
2. Calculate
for each value in the sample:
8
3. Calculate
4. Calculate the standard deviation:
Calculation of π
The equation of a straight line passing though the origin (x=0, y=0) is given by
y=mx
(1.1)
where, m is the slope of the line, x is the independent variable, and y is the dependent variable.
For any round object, the circumference (c) is directly proportional to its diameter (d).
cd
(1.2)
c = d (just like y = m x)
(1.3)
and
where is the constant of proportionality. By measuring the values of c and d of many round
objects and plotting c versus d, one can determine the value of from the slope of the line. You
will use a ruler and vernier caliper to measure the dimensions of c and d. Figure 1.2 shows how
you can read the vernier caliper.
9
Figure 1.2. Vernier caliper (Measurement Uncertainty and Probability, R. Willink)
The uncertainty of this caliper is ± ½ the smallest measurement, or ± 0.05 mm.
Procedure
Be careful when taking any of the measurements to keep errors as small as possible.
Measure the circumference of the given object by using the strip paper and the ruler. Then, use
the vernier caliper to measure the diameter of the five discs. Do this five times using five
different wooden discs. Record your measurements in Table 1.1.
Table 1.1.
c (mm)
d (mm)
=c/d
(-)2
1
2
3
4
5
=
(-)2 =
Questions
1) Calculate , where = (-)2/(N-1)1/2
2) Plot the relation between c and d.
3) Calculate the slope of the graph.
4) What does the slope here represent?
5) Calculate the relative error (see Appendix C), comparing your experimental value with the
theoretical value of = 3.142. Does this agree with your calculated uncertainty?
10
Experiment 2
Basic Electricity and Magnetism
Objectives
1) To study electric charges in a qualitative manner.
2) Explore the fundamental concepts of electrostatics.
3) Explore the fundamental concepts of magnetism.
4) Determine the magnetic field patterns around different types of magnets.
Note: Please, submit one lab report that contains the two parts.
Part One: Basic Electricity
Apparatus
Ebonite (gray) rod, clear rod, a piece of fur, a piece of paper, an electroscope
Introduction
There are two kinds of charges in nature, positive and negative. Positive charges are
carried by protons and negative charges are carried by electrons. When we say an object has a
charge on it, we mean that it has a slight excess of either positive or negative charge. For
instance, in this lab the ebonite rod will be given a negative charge by rubbing it with the fur. We
have not “created” more electrons on the ebonite rod, but rather, have moved some electrons
from the fur onto the rod. In so doing, the fur has excess protons and is positively charged. This
basic fact is commonly referred to as conservation of charge and is a fundamental concept of the
electromagnetic theory.
During this experiment, an electroscope (Figure 2.1) will be charged by two methods,
conduction and induction. To charge the electroscope negatively by conduction, the end of a
charged ebonite rod is touched to the ball on top of the electroscope and electrons flow from the
rod to the ball and the foil leaves, leaving a net negative charge. Because the leaves have like
charges on them, they repel from each other.
To charge the electroscope positively by conduction, the Lucite (clear) or glass rod is
rubbed with silk and touched to the ball on the electroscope. This time electrons flow out of the
electroscope onto the rod leaving a net positive charge on the electroscope foil leaves.
To charge the electroscope negatively by induction, a positively charged rod (Lucite
rubbed with silk) is brought near one side of the ball on top of the electroscope. At the same
time, touch the ball on the opposite side from the charged rod. The positively charged rod causes
a slight polarization on the ball, with electrons being attracted to the rod, leaving more positive
charges than negative on the side of the ball opposite the rod. When you touch the ball, electrons
flow from your finger to the ball, giving the electroscope a net negative charge. When the
charged rod is removed from near the ball, the leaves repel.
11
Figure 2.1. Electroscope (Elementary Lessons in Electricity and Magnetism, Sylvanus P.
Thompson (1881), MacMillan)
Procedure
This experiment is strictly qualitative and involves no calculations. This is, however, an
exercise in observation. You are expected to carefully follow the procedure and describe in
(reasonable) detail your observations. Any deviation from the described procedure will lead to
erroneous results.
Conduction
1) You will be given two plastic rods, a gray one and a clear one. Rub the gray plastic rod
with either the cotton or wool cloth in one direction. Note: If the rods are rubbed in a
back and forth manner they will not be properly charged. Charge the electroscope by
conduction using the gray rod. Draw a picture…
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