Correlation, Causation, and PredictionStatistical calculations focus on analyzing and interpreting scatterplots, creating a scatterplot using statistical software, performing simple regression and correlational analyses, and inferring population characteristics from samples. The world is, to say the least, a complicated place. By using statistics that show us how elements in it are related, we may simplify the manageability of the world and perhaps even be able to predict some future outcomes. In this assignment, you will be helped to understand the relationship of correlation causation and prediction.****************************************BooksReferenceInstructionStatistical reasoning for everyday life.Read Chapters 7 and 8Document/OtherReferenceInstructionChapter 7 Review QuestionsChapter 7 PowerPoint.ppt.pptView PresentationChapter 8 Review QuestionsChapter 8 PowerPoint.ppt.pptView Presentation***************************************Week 5 Lecture Notes:PrintActivity DescriptionAfter you complete the textbook readings, check your understanding of the main concepts by reviewing the chapter review questions in the attached PowerPoint files. Be sure to revisit appropriate sections of the textbook if you find that you need more review. While these questions are not a graded part of this assignment, they are important because they will help you monitor your learning as you progress through the course.â¢Chapter 7 PowerPoint.pptâ¢Chapter 8 PowerPoint.ppt*****************************************Week 5 Assignment: Complete Application Questions and ProblemsActivity DescriptionDownload Data File 4 and complete the problems and questions as presented. Show your work (either your hand calculations or your statistical program output). You may either scan your handwritten work and submit it as a low-resolution graphic, type your answers directly into the document, or cut and paste your work into a Word file. Be sure to name the file using the proper NCU naming conventions before its submittal.Support your paper with a minimum of three (3) scholarly resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included.Length: 5-7 pages not including title and reference pages, may include spreadsheets.Your response should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards where appropriate. Be sure to adhere to Northcentral University’s Academic Integrity Policy.Data File 4
Show all your work
Chapter Seven
Problem 1) Look at the scatterplot below. Does it demonstrate a positive or negative
correlation? Why?
Are there any
outliers? What are they?
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Problem 2) Look at the scatterplot below. Does it demonstrate a positive or negative
correlation? Why?
Are there any outliers? What are
they?
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Problem
3) The following data come from your
book, problem 26 on page 247. Here is
the data:
Mean
daily calories Infant
Mortality Rate (per 1,000 births)
1523 154
3495 6
1941 114
2678 24
1610 107
3443 6
1640 153
3362 7
3429 44
2671
7
a)
For the above data construct a
scatterplot using SPSS or Excel (Follow instructions on page 244 of your
textbook). What does the scatterplot
show? Can you determine a type of
relationship? Are there any outliers
that you can see?
b)
Using the same data conduct a
correlation analysis using SPSS or Excel.
What is the correlation coefficient?
Is it a strong, moderate or weak correlation? Is the correlation significant or not? If it is what does that mean?
Problem 4)
Bill is doing a
project for you in the marketing department.
In conducting his analysis regarding consumer behavior and a new product
that has come out, he tells you the correlation between these two variables is
1.09. What is your response to this
analysis?
Problem 5)
Judy has
conducted an analysis for her supervisor.
The result she obtained was a correlation coefficient that was negative
0.86. Judy is confused by this number
and feels that because it is negative and not positive, is means that it is
bad. You are her supervisor. How would you clarify this result for Judy
regarding the meaning of the correlation?
Problem
6)
Explain
the statement, âcorrelation does not imply causality.â
Problem
7)
Using
the best-fit line below for prediction, answer the following questions:
a)
What would you predict the
price of Product X in volume of 150 to be (approximately)?
b)
What would you predict the
price of Product X in volume of 100 to be (approximately)?
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Problem
8)
You are interested in finding out if
a studentâs ACT score is a good predictor of his or her final college grade
point average (GPA). You have obtained
the following data and are going to conduct a regression analysis with these
figures:
ACT GPA
22.0 3.0
32.0 3.78
33.0 3.68
21.0 2.94
27.0 3.38
25.0 3.21
30.0 3.65
a)
What is the R? What type of relationship does it indicate
(strong/weak; positive/negative)?
b)
Go to the coefficients
readout. The constant is the
intercept. Under that is the ACT and
that is the slope. Using the straight
line formula of Y = mx + b, which you will find on page 262, you will now
predict some future GPA scores: In the
formula (m) is the slope; (x) is the variable that you are looking to use as a
predictor; and (b) is the intercept.
Predict GPA from the following ACT scores using the regression
equation/straight line formula (show all your work):
1)
20
2)
25
3)
34
Chapter Eight
Show all your
work
Problem 1)
A sample of nine
students is selected from among the students taking a particular exam. The nine students were asked how much time
they had spent studying for the exam and the responses (in hours) were as
follows:
18, 7, 10, 13 12, 16, 5, 20, 21
Estimate the
mean study time of all students taking the exam. Round your answer to the nearest tenth of an
hour, if necessary.
Problem 2)
Scores on a
particular test have a mean of 64.6. The
distribution of sample means for samples of size 100 is normal with a mean of
64.6 and a standard deviation of 1.9.
Suppose you take a sample of size 100 of test scores and find that the
mean is 63. What is the z-score
corresponding to this sample mean?
Problem 3)
There are 349
teachers at a college. Among a sample of
110 teachers from this college, 66 have doctorates. Based on this sample, estimate the number of
teachers at this college without doctorates.
Problem 4)
Sample size =
400; sample mean = 44; sample standard deviation = 16. What is the margin of error?
Problem 5)
A sample of 64
statistics students at a small college had a mean mathematics ACT score of 28
with a standard deviation of 4. Estimate
the mean mathematics ACT score for all statistics students at this
college. Give the 95% confidence
interval.
Problem 6)
A government
survey conducted to estimate the mean price of houses in a metropolitan area is
designed to have a margin of error of $10,000.
Pilot studies suggest that the population standard deviation is
$70,000. Estimate the minimum sample
size needed to estimate the population mean with the stated accuracy.
Problem 7)
A researcher
wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that
33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95%
confidence interval.
