it basic statistic quiz and homework, around 30 questions
needed done in 2 hours
ill give you the infor to log in and do the work
90 percent score up
attachment are some questions in homework
Category: Mathematics
Divide the number of times something happens
by the number of times it could happen.
Explain to your classmates how you interpret/understand this statement.
1 paragraph please
Question: Study and write a short paragraph explaining what you learned from each of the following 3 lectures. Correctly answering questions related to Statistics content earns you extra credit!
1 Learning Objectives
- Distinguish between a sample and a population
- Define inferential statistics
- Identify biased samples
- Distinguish between simple random sampling and stratified sampling
- Distinguish between random sampling and random assignment
Populations and samples
In statistics, we often rely on a sample — that is, a small subset of a larger set of data — to draw inferences about the larger set. The larger set is known as the population from which the sample is drawn.
Example #1: You have been hired by the National Election Commission to examine how the American people feel about the fairness of the voting procedures in the U.S. Whom will you ask?
It is not practical to ask every single American how he or she feels about the fairness of the voting procedures. Instead, we query a relatively small number of Americans, and draw inferences about the entire country from their responses. The Americans actually queried constitute our sample of the larger population of all Americans. The mathematical procedures whereby we convert information about the sample into intelligent guesses about the population fall under the rubric of inferential statistics.
A sample is typically a small subset of the population. In the case of voting attitudes, we would sample a few thousand Americans drawn from the hundreds of millions that make up the country. In choosing a sample, it is therefore crucial that it not over-represent one kind of citizen at the expense of others. For example, something would be wrong with our sample if it happened to be made up entirely of Florida residents. If the sample held only Floridians, it could not be used to infer the attitudes of other Americans. The same problem would arise if the sample were comprised only of Republicans. Inferential statistics are based on the assumption that sampling is random. We trust a random sample to represent different segments of society in close to the appropriate proportions (provided the sample is large enough; see below).
Example #2: We are interested in examining how many math classes have been taken on average by current graduating seniors at American colleges and universities during their four years in school. Whereas our population in the last example included all US citizens, now it involves just the graduating seniors throughout the country. This is still a large set since there are thousands of colleges and universities, each enrolling many students. (New York University, for example, enrolls 48,000 students.) It would be prohibitively costly to examine the transcript of every college senior. We therefore take a sample of college seniors and then make inferences to the entire population based on what we find. To make the sample, we might first choose some public and private colleges and universities across the United States. Then we might sample 50 students from each of these institutions. Suppose that the average number of math classes taken by the people in our sample were 3.2. Then we might speculate that 3.2 approximates the number we would find if we had the resources to examine every senior in the entire population. But we must be careful about the possibility that our sample is non-representative of the population. Perhaps we chose an overabundance of math majors, or chose too many technical institutions that have heavy math requirements. Such bad sampling makes our sample unrepresentative of the population of all seniors.
To solidify your understanding of sampling bias, consider the following example. Try to identify the population and the sample, and then reflect on whether the sample is likely to yield the information desired.
Example #3: A substitute teacher wants to know how students in the class did on their last test. The teacher asks the 10 students sitting in the front row to state their latest test score. He concludes from their report that the class did extremely well. What is the sample? What is the population? Can you identify any problems with choosing the sample in the way that the teacher did?
In Example #3, the population consists of all students in the class. The sample is made up of just the 10 students sitting in the front row. The sample is not likely to be representative of the population. Those who sit in the front row tend to be more interested in the class and tend to perform higher on tests. Hence, the sample may perform at a higher level than the population.
Example #4: A coach is interested in how many cartwheels the average college freshmen at his university can do. Eight volunteers from the freshman class step forward. After observing their performance, the coach concludes that college freshmen can do an average of 16 cartwheels in a row without stopping.
In Example #4, the population is the class of all freshmen at the coach’s university. The sample is composed of the 8 volunteers. The sample is poorly chosen because volunteers are more likely to be able to do cartwheels than the average freshman; people who can’t do cartwheels probably did not volunteer! In the example, we are also not told of the gender of the volunteers. Were they all women, for example? That might affect the outcome, contributing to the non-representative nature of the sample (if the school is co-ed).
Sampling Bias is Discussed in More Detail
Simple Random Sampling
Researchers adopt a variety of sampling strategies. The most straightforward is simple random sampling. Such sampling requires every member of the population to have an equal chance of being selected into the sample. In addition, the selection of one member must be independent of the selection of every other member. That is, picking one member from the population must not increase or decrease the probability of picking any other member (relative to the others). In this sense, we can say that simple random sampling chooses a sample by pure chance. To check your understanding of simple random sampling, consider the following example. What is the population? What is the sample? Was the sample picked by simple random sampling? Is it biased?
Example #5: A research scientist is interested in studying the experiences of twins raised together versus those raised apart. She obtains a list of twins from the National Twin Registry, and selects two subsets of individuals for her study. First, she chooses all those in the registry whose last name begins with Z. Then she turns to all those whose last name begins with B. Because there are so many names that start with B, however, our researcher decides to incorporate only every other name into her sample. Finally, she mails out a survey and compares characteristics of twins raised apart versus together.
In Example #5, the population consists of all twins recorded in the National Twin Registry. It is important that the researcher only make statistical generalizations to the twins on this list, not to all twins in the nation or world. That is, the National Twin Registry may not be representative of all twins. Even if inferences are limited to the Registry, a number of problems affect the sampling procedure we described. For instance, choosing only twins whose last names begin with Z does not give every individual an equal chance of being selected into the sample. Moreover, such a procedure risks over-representing ethnic groups with many surnames that begin with Z. There are other reasons why choosing just the Z’s may bias the sample. Perhaps such people are more patient than average because they often find themselves at the end of the line! The same problem occurs with choosing twins whose last name begins with B. An additional problem for the B’s is that the every-other-one procedure disallowed adjacent names on the B part of the list from being both selected. Just this defect alone means the sample was not formed through simple random sampling.
Sample size matters
Recall that the definition of a random sample is a sample in which every member of the population has an equal chance of being selected. This means that the sampling procedure rather than the results of the procedure define what it means for a sample to be random. Random samples, especially if the sample size is small, are not necessarily representative of the entire population. For example, if a random sample of 20 subjects were taken from a population with an equal number of males and females, there would be a nontrivial probability (0.06) that 70% or more of the sample would be female. (To see how to obtain this probability, see the .) Such a sample would not be representative, although it would be drawn randomly. Only a large sample size makes it likely that our sample is close to representative of the population. For this reason, inferential statistics take into account the sample size when generalizing results from samples to populations. In later chapters, you’ll see what kinds of mathematical techniques ensure this sensitivity to sample size.
More complex sampling
Sometimes it is not feasible to build a sample using simple random sampling. To see the problem, consider the fact that both Dallas and Houston are competing to be hosts of the 2012 Olympics. Imagine that you are hired to assess whether most Texans prefer Houston to Dallas as the host, or the reverse. Given the impracticality of obtaining the opinion of every single Texan, you must construct a sample of the Texas population. But now notice how difficult it would be to proceed by simple random sampling. For example, how will you contact those individuals who dont vote and dont have a phone? Even among people you find in the telephone book, how can you identify those who have just relocated to California (and had no reason to inform you of their move)? What do you do about the fact that since the beginning of the study, an additional 4,212 people took up residence in the state of Texas? As you can see, it is sometimes very difficult to develop a truly random procedure. For this reason, other kinds of sampling techniques have been devised. We now discuss two of them.
Random Assignment
In experimental research, populations are often hypothetical. For example, in an experiment comparing the effectiveness of a new anti-depressant drug with a placebo, there is no actual population of individuals taking the drug. In this case, a specified population of people with some degree of depression is defined and a random sample is taken from this population. The sample is then randomly divided into two groups; one group is assigned to the treatment condition (drug) and the other group is assigned to the control condition (placebo). This random division of the sample into two groups is called random assignment. Random assignment is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first 20 subjects to show up at the experiment were assigned to the experimental group and the second 20 subjects were assigned to the control group. It is possible that subjects who show up late tend to be more depressed than those who show up early, thus making the experimental group less depressed than the control group even before the treatment was administered.
In experimental research of this kind, failure to assign subjects randomly to groups is generally more serious than having a non-random sample. Failure to randomize (the former error) invalidates the experimental findings. A non-random sample (the latter error) simply restricts the generalizability of the results.
Stratified Sampling
Since simple random sampling often does not ensure a representative sample, a sampling method called stratified random sampling is sometimes used to make the sample more representative of the population. This method can be used if the population has a number of distinct “strata” or groups. In stratified sampling, you first identify members of your sample who belong to each group. Then you randomly sample from each of those subgroups in such a way that the sizes of the subgroups in the sample are proportional to their sizes in the population.
Let’s take an example: Suppose you were interested in views of capital punishment at an urban university. You have the time and resources to interview 200 students. The student body is diverse with respect to age; many older people work during the day and enroll in night courses (average age is 39), while younger students generally enroll in day classes (average age of 19). It is possible that night students have different views about capital punishment than day students. If 70% of the students were day students, it makes sense to ensure that 70% of the sample consisted of day students. Thus, your sample of 200 students would consist of 140 day students and 60 night students. The proportion of day students in the sample and in the population (the entire university) would be the same. Inferences to the entire population of students at the university would therefore be more secure.
2 Learning Objectives
- Define and distinguish between independent and dependent variables
- Define and distinguish between discrete and continuous variables
- Define and distinguish between qualitative and quantitative variables
Independent and dependent variables
Variables are properties or characteristics of some event, object, or person that can take on different values or amounts (as opposed to constants such as that do not vary). When conducting research, experimenters often manipulate variables. For example, an experimenter might compare the effectiveness of four types of antidepressants. In this case, the variable is “type of antidepressant.” When a variable is manipulated by an experimenter, it is called an independent variable. The experiment seeks to determine the effect of the independent variable on relief from depression. In this example, relief from depression is called a dependent variable. In general, the independent variable is manipulated by the experimenter and its effects on the dependent variable are measured.
Example #1: Can blueberries slow down aging? A study indicates that antioxidants found in blueberries may slow down the process of aging. In this study, 19-month-old rats (equivalent to 60-year-old humans) were fed either their standard diet or a diet supplemented by either blueberry, strawberry, or spinach powder. After eight weeks, the rats were given memory and motor skills tests. Although all supplemented rats showed improvement, those supplemented with blueberry powder showed the most notable improvement.
1. What is the independent variable? (dietary supplement: none, blueberry, strawberry, and spinach)
2. What are the dependent variables? (memory test and motor skills test)
More information on the blueberry study
Example #2: Does beta-carotene protect against cancer? Beta-carotene supplements have been thought to protect against cancer. However, a study published in the Journal of the National Cancer Institute suggests this is false. The study was conducted with 39,000 women aged 45 and up. These women were randomly assigned to receive a beta-carotene supplement or a placebo, and their health was studied over their lifetime. Cancer rates for women taking the beta-carotene supplement did not differ systematically from the cancer rates of those women taking the placebo.
1. What is the independent variable? (supplements: beta-carotene or placebo)
2. What is the dependent variable? (occurrence of cancer)
Example #3: How bright is right? An automobile manufacturer wants to know how bright brake lights should be in order to minimize the time required for the driver of a following car to realize that the car in front is stopping and to hit the brakes.
1. What is the independent variable? (brightness of brake lights)
2. What is the dependent variable? (time to hit brakes)
Levels of an Independent Variable
If an experiment compares an experimental treatment with a control treatment, then the independent variable (type of treatment) has two levels: experimental and control. If an experiment were comparing five types of diets, then the independent variable (type of diet) would have 5 levels. In general, the number of levels of an independent variable is the number of experimental conditions.
Qualitative and Quantitative Variables
An important distinction between variables is between qualitative variables and quantitative variables. Qualitative variables are those that express a qualitative attribute such as hair color, eye color, religion, favorite movie, gender, and so on. The values of a qualitative variable do not imply a numerical ordering. Values of the variable religion differ qualitatively; no ordering of religions is implied. Qualitative variables are sometimes referred to as categorical variables. Quantitative variables are those variables that are measured in terms of numbers. Some examples of quantitative variables are height, weight, and shoe size.
In the study on the effect of diet discussed , the independent variable was type of supplement: none, strawberry, blueberry, and spinach. The variable “type of supplement” is a qualitative variable; there is nothing quantitative about it. In contrast, the dependent variable “memory test” is a quantitative variable since memory performance was measured on a quantitative scale (number correct).
Discrete and Continuous Variables
Variables such as number of children in a household are called discrete variables since the possible scores are discrete points on the scale. For example, a household could have three children or six children, but not 4.53 children. Other variables such as “time to respond to a question” are continuous variables since the scale is continuous and not made up of discrete steps. The response time could be 1.64 seconds, or it could be 1.64237123922121 seconds. Of course, the practicalities of measurement preclude most measured variables from being truly continuous.
3 Learning Objectives
- Define and distinguish among nominal, ordinal, interval, and ratio scales
- Identify a scale type
- Discuss the type of scale used in psychological measurement
- Give examples of errors that can be made by failing to understand the proper use of measurement scales
Types of Scales
Before we can conduct a statistical analysis, we need to measure our dependent variable. Exactly how the measurement is carried out depends on the type of variable involved in the analysis. Different types are measured differently. To measure the time taken to respond to a stimulus, you might use a stop watch. Stop watches are of no use, of course, when it comes to measuring someone’s attitude towards a political candidate. A rating scale is more appropriate in this case (with labels like “very favorable,” “somewhat favorable,” etc.). For a dependent variable such as “favorite color,” you can simply note the color-word (like “red”) that the subject offers.
Although procedures for measurement differ in many ways, they can be classified using a few fundamental categories. In a given category, all of the procedures share some properties that are important for you to know about. The categories are called “scale types,” or just “scales,” and are described in this section.
Nominal scales
When measuring using a nominal scale, one simply names or categorizes responses. Gender, handedness, favorite color, and religion are examples of variables measured on a nominal scale. The essential point about nominal scales is that they do not imply any ordering among the responses. For example, when classifying people according to their favorite color, there is no sense in which green is placed “ahead of” blue. Responses are merely categorized. Nominal scales embody the lowest level of measurement.
Ordinal scales
A researcher wishing to measure consumers’ satisfaction with their microwave ovens might ask them to specify their feelings as either “very dissatisfied,” “somewhat dissatisfied,” “somewhat satisfied,” or “very satisfied.” The items in this scale are ordered, ranging from least to most satisfied. This is what distinguishes ordinal from nominal scales. Unlike nominal scales, ordinal scales allow comparisons of the degree to which two subjects possess the dependent variable. For example, our satisfaction ordering makes it meaningful to assert that one person is more satisfied than another with their microwave ovens. Such an assertion reflects the first person’s use of a verbal label that comes later in the list than the label chosen by the second person.
On the other hand, ordinal scales fail to capture important information that will be present in the other scales we examine. In particular, the difference between two levels of an ordinal scale cannot be assumed to be the same as the difference between two other levels. In our satisfaction scale, for example, the difference between the responses “very dissatisfied” and “somewhat dissatisfied” is probably not equivalent to the difference between “somewhat dissatisfied” and “somewhat satisfied.” Nothing in our measurement procedure allows us to determine whether the two differences reflect the same difference in psychological satisfaction. Statisticians express this point by saying that the differences between adjacent scale values do not necessarily represent equal intervals on the underlying scale giving rise to the measurements. (In our case, the underlying scale is the true feeling of satisfaction, which we are trying to measure.)
What if the researcher had measured satisfaction by asking consumers to indicate their level of satisfaction by choosing a number from one to four? Would the difference between the responses of one and two necessarily reflect the same difference in satisfaction as the difference between the responses two and three? The answer is No. Changing the response format to numbers does not change the meaning of the scale. We still are in no position to assert that the mental step from 1 to 2 (for example) is the same as the mental step from 3 to 4.
Interval scales
Interval scales are numerical scales in which intervals have the same interpretation throughout. As an example, consider the Fahrenheit scale of temperature. The difference between 30 degrees and 40 degrees represents the same temperature difference as the difference between 80 degrees and 90 degrees. This is because each 10-degree interval has the same physical meaning (in terms of the kinetic energy of molecules).
Interval scales are not perfect, however. In particular, they do not have a true zero point even if one of the scaled values happens to carry the name “zero.” The Fahrenheit scale illustrates the issue. Zero degrees Fahrenheit does not represent the complete absence of temperature (the absence of any molecular kinetic energy). In reality, the label “zero” is applied to its temperature for quite accidental reasons connected to the history of temperature measurement. Since an interval scale has no true zero point, it does not make sense to compute ratios of temperatures. For example, there is no sense in which the ratio of 40 to 20 degrees Fahrenheit is the same as the ratio of 100 to 50 degrees; no interesting physical property is preserved across the two ratios. After all, if the “zero” label were applied at the temperature that Fahrenheit happens to label as 10 degrees, the two ratios would instead be 30 to 10 and 90 to 40, no longer the same! For this reason, it does not make sense to say that 80 degrees is “twice as hot” as 40 degrees. Such a claim would depend on an arbitrary decision about where to “start” the temperature scale, namely, what temperature to call zero (whereas the claim is intended to make a more fundamental assertion about the underlying physical reality).
Ratio scales
The ratio scale of measurement is the most informative scale. It is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured. You can think of a ratio scale as the three earlier scales rolled up in one. Like a nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on the scale also carries the same meaning.
The Fahrenheit scale for temperature has an arbitrary zero point and is therefore not a ratio scale. However, zero on the Kelvin scale is absolute zero. This makes the Kelvin scale a ratio scale. For example, if one temperature is twice as high as another as measured on the Kelvin scale, then it has twice the kinetic energy of the other temperature.
Another example of a ratio scale is the amount of money you have in your pocket right now (25 cents, 55 cents, etc.). Money is measured on a ratio scale because, in addition to having the properties of an interval scale, it has a true zero point: if you have zero money, this implies the absence of money. Since money has a true zero point, it makes sense to say that someone with 50 cents has twice as much money as someone with 25 cents (or that Bill Gates has a million times more money than you do).
What level of measurement is used for psychological variables?
Rating scales are used frequently in psychological research. For example, experimental subjects may be asked to rate their level of pain, how much they like a consumer product, their attitudes about capital punishment, their confidence in an answer to a test question. Typically these ratings are made on a 5-point or a 7-point scale. These scales are ordinal scales since there is no assurance that a given difference represents the same thing across the range of the scale. For example, there is no way to be sure that a treatment that reduces pain from a rated pain level of 3 to a rated pain level of 2 represents the same level of relief as a treatment that reduces pain from a rated pain level of 7 to a rated pain level of 6.
In memory experiments, the dependent variable is often the number of items correctly recalled. What scale of measurement is this? You could reasonably argue that it is a ratio scale. First, there is a true zero point: some subjects may get no items correct at all. Moreover, a difference of one represents a difference of one item recalled across the entire scale. It is certainly valid to say that someone who recalled 12 items recalled twice as many items as someone who recalled only 6 items.
But number-of-items recalled is a more complicated case than it appears at first. Consider the following example in which subjects are asked to remember as many items as possible from a list of 10. Assume that (a) there are 5 easy items and 5 difficult items, (b) half of the subjects are able to recall all the easy items and different numbers of difficult items, while (c) the other half of the subjects are unable to recall any of the difficult items but they do remember different numbers of easy items. Some sample data are shown below.
Subject
Easy Items
Difficult Items
Score
A
0
0
1
1
0
0
0
0
0
0
2
B
1
0
1
1
0
0
0
0
0
0
3
C
1
1
1
1
1
1
1
0
0
0
7
D
1
1
1
1
1
0
1
1
0
1
8
Let’s compare (1) the difference between Subject A’s score of 2 and Subject B’s score of 3 with (2) the difference between Subject C’s score of 7 and Subject D’s score of 8. The former difference is a difference of one easy item; the latter difference is a difference of one difficult item. Do these two differences necessarily signify the same difference in memory? We are inclined to respond “No” to this question since only a little more memory may be needed to retain the additional easy item whereas a lot more memory may be needed to retain the additional hard item. The general point is that it is often inappropriate to consider psychological measurement scales as either interval or ratio.
Consequences of level of measurement
Why are we so interested in the type of scale that measures a dependent variable? The crux of the matter is the relationship between the variable’s level of measurement and the statistics that can be meaningfully computed with that variable. For example, consider a hypothetical study in which 5 children are asked to choose their favorite color from blue, red, yellow, green, and purple. The researcher codes the results as follows:
Color
Code
Blue
Red
Yellow
Green
Purple
1
2
3
4
5
This means that if a child said her favorite color was “Red,” then the choice was coded as “2,” if the child said her favorite color was “Purple,” then the response was coded as 5, and so forth. Consider the following hypothetical data:
Subject
Color
Code
1
2
3
4
5
Blue
Blue
Green
Green
Purple
1
1
4
4
5
Each code is a number, so nothing prevents us from computing the average code assigned to the children. The average happens to be 3, but you can see that it would be senseless to conclude that the average favorite color is yellow (the color with a code of 3). Such nonsense arises because favorite color is a nominal scale, and taking the average of its numerical labels is like counting the number of letters in the name of a snake to see how long the beast is.
Does it make sense to compute the mean of numbers measured on an ordinal scale? This is a difficult question, one that statisticians have debated for decades. You will be able to explore this issue yourself in a simulation shown in the next section and reach your own conclusion. The prevailing (but by no means unanimous) opinion of statisticians is that for almost all practical situations, the mean of an ordinally-measured variable is a meaningful statistic. However, as you will see in the simulation, there are extreme situations in which computing the mean of an ordinally-measured variable can be very misleading.
20 Slides PPT Statistics assignment. Due in 18 hours. No Plagiarism.
Check the link below for the instruction file.
https://drive.google.com/file/d/1BGQOKL05mtDjlyzvN_XLxr8NVoF_TO-Z/view?usp=sharing
Check the link below for the data file.
https://drive.google.com/file/d/1tg8FInb_-DZNk-x4ZFpO7Dacp_1W-mYe/view?usp=sharing
Semester 2 Research Project: Proofs
Student number:
Overview: The purpose of this project is to prove a few geometric theorems. The project is
divided into two activities, each requiring one proof. The proofs will relate to topics that you’ll
cover in future chapters. The first proof will be a three-part, two-column proof. The next will be
a paragraph proof.
Your online textbook will be an invaluable reference for this project. In each activity,
the research section will identify the portion of your textbook most applicable to the required
proof.
Instructions: To complete the project, you’ll fill in the text boxes (for example, ) with
your answers. This file is set up as a reader-enabled form. This means you can only enter
content into the required fields. To navigate through the file, hit tab or click in the text boxes to
enter your answers. Hitting tab will take you to each of the fields you need to complete for the
project. Often, before entering your answers in the text boxes, you’ll need to do some work on
scratch paper.
Once you have filled in all your answers, choose Save As from the File menu. Include your
student number in the file name before you upload your assignment to Penn Foster. For
example, the file you downloaded the file named student-number_0236B12S.pdf. When the
window appears to “Save As,” include your student number in the file name
(12345678_0236B12S.pdf), where 12345678 is your eight-digit student number).
Course title and number: MA02B01
Assignment number: 0236B12S
Page 1 of 4
Activity 1: Proof of the SSS Similarity Theorem
Theorem 8.3.2: If the three sides in one triangle are proportional to the three sides in another
triangle, then the triangles are similar.
Setup: On scratch paper, draw two triangles with one larger than the other and the sides of one
triangle proportional to the other. Label the larger triangle ABC and the smaller triangle DEF so
that
Given: The sides of triangle ABC are proportional to the sides of triangle DEF so that
Prove: Triangle ABC is similar to triangle DEF.
Research: In your online textbook, study Chapter 8 to understand properties of similarity. If
necessary, review reasoning and proof in Chapter 2, properties of parallel lines in Chapter 3, and
triangle congruence in Chapter 4. To complete this proof, you may use any definition, postulate,
or theorem in your online textbook on or before page 517.
Statements
1. Segment GH is parallel to segment BC.
2. Segment AB and AC are to
segments GH and BC.
3. Angle AGH is to angle ABC,
and angle AHG is congruent to angle ACB.
4. Triangle AGH is to triangle ABC.
Reasons
1. By
2. Definition of a
3. Angles Postulate
4. AA Property
Page 2 of 4
Proof:
Part 1: Construct segment GH in triangle ABC so that G is between A and B, AG = DE, and
segment GH is parallel to segment BC. (Hint: You should actually do this on your setup
figure.) Show that triangle AGH is similar to triangle ABC.
Part 2: Show that triangle AGH is congruent to triangle DEF.
Page 3 of 4
Statements
1. Triangle AGH is to triangle ABC.
2. The sides of triangle AGH are
to the sides of triangle ABC.
3. The sides of triangle ABC are proportional to
the sides of triangle DEF.
4. The sides of triangle AGH are
to the sides of triangle DEF.
5.
6. AG = DE
7. GH = EF and HA = FD
8. Triangle AGH is to triangle DEF.
Reasons
1. Result from Part 1
2. Polygon Postulate
3.
4. Property
5. Definition of sides
6. By
7. Transitive Property
8. Congruency Postulate
Part 3: Show the required result.
Statements
1. Triangle AGH is to triangle DEF.
2. Angle AGH is to angle DEF, and
angle GAH is congruent to angle EDF.
3. Angle AGH is congruent to angle ABC, and
angle AHG is to angle ACB.
4. Angle ABC is to angle DEF, and
angle ACD is congruent to angle EDF.
5. Triangle ABC is to triangle DEF.
Reasons
1. Result from Part 2
2.
3. Repeat of statement shown in Part 1
4. Property
5. AA Property
Note: You can prove the SAS Similarity Theorem in like fashion.
Activity 2: Proof of the Converse of the Chords and Arcs Theorem
Theorem 9.1.6: In a circle or in congruent circles, the chords of congruent arcs are congruent.
Setup: On scratch paper, construct congruent circles with centers at P and M. Then construct
congruent arcs QR on circle P and NO on circle M. Finally, draw triangles PQR and MNO.
Research: In your online textbook, study Chapter 9 to understand the properties of arcs and
circles in general. If necessary, review reasoning and proof in Chapter 2 and triangle congruence
in Chapter 4. To complete this proof, you may use any postulate or theorem on or before 568 in
your online textbook.
Proof: Since QR and NO are , angle QPR is congruent to angle NMO by the
of the degree measure of arcs.
Segments PQ, PR, MN, and MO are all of congruent circles, so they are all .
In particular, segment PQ is to segment MN and segment PR is congruent to
MO.
Therefore, triangle PQR is to triangle MNO by . Consequently, segment QR
is congruent to segment NO by , which proves that, in a
or in congruent circles, the of congruent are congruent.
Due in 24 hours. No Plagiarism. Check the link below for the instruction file.
https://drive.google.com/file/d/1BGQOKL05mtDjlyzvN_XLxr8NVoF_TO-Z/view?usp=sharing
Check the link below for the data file.
https://drive.google.com/file/d/1tg8FInb_-DZNk-x4ZFpO7Dacp_1W-mYe/view?usp=sharing
Due in 18 hours. No Plagirism. Turnintin Report is must.
Scenario: Consider your last big purchase such as a car, appliances, home repairs, home purchase, computer equipment, college tuition, or another “big-ticket” item, which are often purchased using loans/financing (by borrowing money). Also consider your decision-making process that led you to choose a particular make, model, or brand of the product (or service) you purchased and whether it was the right time to make the purchase given economic conditions at the time of your purchase. While analyzing your decision, keep in mind everything from interest rates to the prices of complementary and substitute goods are driven by human economic behavior.
Develop a minimum 1,050-word analysis of your decision-making process in which you include the following:
- Retrieve statistics on Real Gross Domestic Product (GDP) and on Real Personal Consumption Expenditures (PCE) by year for the last ten years. You can retrieve those statistics from internet sources including, but not limited to, the Federal Reserve of St. Louis’s FRED web site, the U.S. Department of Commerce’s Bureau of Economic Analysis (BEA) web site, or another credible source of your choice. Post these statistics in a single worksheet of an Excel workbook and submit your Excel file with your report. In your report, discuss the latest 10-year trends in both GDP and PCE. Also discuss how the trends in GDP compare with trends in PCE. You are encouraged to include graphs of these statistics in your report; you could create the graphs in Exceland copy them into your report.
- Retrieve statistics on the Effective Federal Funds Rate and on the Consumer Price Index: All Items Less Food and Energy by year for the last 30 years. You can retrieve those statistics from internet sources including, but not limited to, the Federal Reserve of St. Louis’s FRED web site, the U.S. Department of Labor’s Bureau of Labor Statistics (BLS) web site, or other credible sources of your choice. Post these statistics in a single worksheet of an Excel workbook and submit your Excel file with your report. In your report, discuss how the trends in the Effective Federal Funds Rate compare with trends in inflation. If you took out a loan to pay for your “big-ticket” purchase, what was the interest rate on your loan? Were interest rates rising or falling at that time? Were interest rates relatively high or low at that time? You are also encouraged to include graphs of these statistics in your report.
- Discuss the influence of any Federal government or state government programs, such as tax credits or tax deductions for energy-saving/efficiency purchases, on your decision to make your last big purchase; or if government incentives did not factor into your decision, explain why not.
- Develop conclusions about the economy’s influence on personal and business decision-making relative to purchases of big-ticket items, investments, or other major purchases.
Cite a minimum of three peer-reviewed sources. Note: The Federal Reserve of St. Louis, the Bureau of Economic Analysis, and the Bureau of Labor Statistics can be cited to fulfill this requirement.
Format your paper consistent with APA guidelines.
Please go through the problem statement and find the Dataset attached in the Project Section.
Dataset: Coffee Cafe Night (Attached)
“The data set provided to you is the data set of a Caf Chain for one of its restaurants. Do a thorough analysis of the data and come up with the following analysis and present it in a powerpoint deck of 10 20 slides.
The owner of the restaurant wants you to use this data to come up with a set of recommendations that can help his Caf Chain increase his revenues. He has not been able to launch a loyalty program and is unable to provide you with a data set that has customer level information. But, he is able to provide you with a data set for POS (point of sale data) for one of his chains.
- Exploratory Analysis (45 Marks)
- Exploratory Analysis of data & an executive summary of your top findings, supported by graphs. 15 Marks
- What kind of trends do you notice in terms of consumer behavior over different times of the day and different days of the week? Can you give concrete recommendations based on the same? 10 Marks
- Are there certain menu items that can be taken off the menu? 10 Marks
- Are there trends across months that you are able to notice? 10 Marks
- Menu Analysis– (45 Marks)
- Identify the most popular combos that can be suggested to the restaurant chain after a thorough analysis of the most commonly occurring sets of menu items in the customer orders. The restaurant doesnt have any combo meals. Can you suggest the best combo meals? 45 Marks
Please note the following:
- Your submission:should be a PowerPoint Presentation (Deck of 19- 20 slides). Appendices are not counted in the word limit.
- You must give the sources of data presented. Do not refer to blogs; Wikipedia etc.
- Please ensure timely submission as post-deadline assignment will not be accepted.
Scoring guide (Rubric) – Rubric (3)
CriteriaPointsExploratory Analysis of data & executive summary of your top findings, supported by graphs.f criterion15What kind of trends do you notice in terms of consumer behavior over different times of the day and different days of the week? Can you give concrete recommendations based on the same? on10Are there certain menu items that can be taken off the menu?10Are there trends across months that you are able to notice?erion10Identify the most popular combos that can be suggested to the restaurant chain after a thorough analysis of the most commonly occurring sets of menu items in the customer orders. The restaurant doesnt have any combo meals. Can you suggest the best combo meals?45Points90
PART 1:
The following table shows the number of marriages in a given State broken down by age groups and gender:
AGE at the time of the marriage
Less than 20
20-24
25-34
35-44
45 +
Total
Male
505
7,760
27,072
10,950
12,173
Female
1,252
11,405
27,632
9,651
10,352
Totals
Use the table to answer questions (1) to (11).
1. Use the information in the table to fill in the blanks in the row and column totals.
2. How many people (male and female) got married in the State?
3. If a person that was married was randomly chosen, what is the probability that the person was a female less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.
4. If a person that was married was randomly chosen, what is the probability that the person was a male less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.5. If a person that was married was randomly chosen, what is the probability that the person was between the ages of 25 and 34? Express your answer as a percent rounded to the nearest whole percent.
6. Of the people over the age of 45 who got married, what percentage was female? What percentage was male? Express your answer as a percent rounded to the nearest whole percent.
7. Given that a person married was less than twenty years old, what is the probability that the person was male?
8. Given that a person married was female, what is the probability that the person was between the ages of 35 and 44?
9. If a person that was married was randomly chosen, what is the probability that the person was over the age of 45 or female?
10. If a person that was married was randomly chosen, what is the probability that the person is male and between the ages of 25 and 34?
11. Describe two events, A and B, which are mutually exclusive for the number of marriages in the State. Calculate the probability of each event, and the probability of A or B occurring.
12. Go to the state of Michigans website () and search on Vital Statistics. Here you will find several categories containing interesting statistics about the state of Michigan. Which statistic or statistics from the website do you find interesting? Explain why you find it interesting. What information or story do the statistics tell you? Write 2-3 paragraphs summarizing the statistics. Is there any information lacking that might make the statistic more meaningful? Why or why not?
PART 2:
There are data that give the relative frequency probabilities of various types of accidents (such as being killed by lightning, by a shark bite, or by falling airplane debris).
Choose two types of fatal accidents and research the relative frequency probabilities of each. Compare and discuss your findings. Were you surprised by the results? Why or why not?Your answers should be a minimum of three complete sentences. Be sure to include your references.
Defina y suministre ejemplos:
regresin lineal simple
Correlacin
coeficiente de correlacin
estimacin de los prametros de regresin (coeficiente y pendiente)
prueba de hiptesis para regresin lineal simple
