Download Division of Mathematics, HCC Course Objectives for Chapter 2

Howard Community College
Math 138 – Statistics
Course Objectives
Written in Power Point format
Michael O’Donnell
Legend (colors used)
• Blue : Part of the syllabus
• Green: Not part of the syllabus but an important
statistical or applied topic that will be covered if
time permits
• Violet: Not explicitly listed in the syllabus, but I
have seen questions covering this topic on past
tests, and so will be covered.
• Brown: Listed in the syllabus and covered in
class, and may be required for homework, but
normally not on tests.
Division of Mathematics, HCC
Course Objectives for Chapter 2
After studying this chapter, the student will be able
to:
1. Determine the context for the data values.
•
Identify the six W’s in any data set: Who, What,
When, Where, Why, How.
2. Identify the cases and variables in any data set.
3. Classify a variable as categorical or
quantitative. Identify units for quantitative data.
4. Identify the population from which a sample
was chosen.
Division of Mathematics, HCC
Course Objectives for Chapter 3
After studying this chapter, the student will be able to:
5. Appropriately display categorical data using a
frequency table, bar chart, or pie chart.
6. Using a contingency table, determine marginal
and conditional distributions, noting any
anomalies or extraordinary features revealed by
the display of a variable.
• Recognize when events are independent.
• Recognize a situation that involves Simpson’s
Paradox.
Division of Mathematics, HCC
Course Objectives for Chapter 4
After studying this chapter, the student will be able to:
7.
Appropriately display quantitative data using a frequency distribution,
histogram, relative frequency histogram, stem-and-leaf display,
dotplot.
8.
Describe the general shape of a distribution in terms of shape, center
and spread.
9.
Describe any anomalies or extraordinary features revealed by the
display of a variable.
10. Compute and apply the concepts of mean and median to a set of
data.
11. Compute and apply the concept of the standard deviation and IQR to
a set of data.
12. Select a suitable measure of center/spread for a variable based on
information about its distribution.
13. Create a five-number summary of a variable.
Division of Mathematics, HCC
Course Objectives for Chapter 5
After studying this chapter, the student will be able to:
14. Construct a boxplot by hand.
15. Construct side-by-side boxplots for two or more groups.
16. Construct side by side histograms on comparable
scales to compare the distributions of two groups.
17. Compare the distributions of two or more groups by
comparing their shapes, centers, spreads, and unusual
features.
18. Use the 1.5 IQR rule to identify possible outliers.
19. Display quantitative data over time using a timeplot.
Division of Mathematics, HCC
Course Objectives for Chapter 6
After studying this chapter, the student will be able to:
20. Compare values from two different distributions using their zscores.
21. Use Normal models (when appropriate) and the 68-95-99.7
Rule to estimate the percentage of observations falling
within one, two, or three standard deviations of the mean.
22. Determine the percentages of observations that satisfy
certain conditions by using the Normal model and determine
“extraordinary” values, and the reverse.
23. Determine whether a variable satisfies the Nearly Normal
condition by making a normal probability plot or histogram.
•
Note: It is essential that this chapter be mastered. Almost
everything in Unit 3 depends on it.
Division of Mathematics, HCC
Course Objectives for Chapter 7
After studying this chapter, the student will be able
to:
24. Use a scatterplot to determine if a linear
correlation is suggested between two
variables and describe the correlation with
regard to direction, form and scatter.
25. Compute the correlation of two variables and
use it as part of the description of a
scatterplot.
26. Identify and describe points that deviate from
the overall pattern.
Division of Mathematics, HCC
Course Objectives for Chapter 8
After studying this chapter, the student will be able to:
27. Compute a linear equation that models the
relationship between two variables.
28. Determine whether the slope of a regression line
makes sense and interpret the slope in the context of
the problem.
29. Know how to use a plot of residuals against predicted
values to check the straight enough condition or look
for outliers.
30. Find the residual for a given x.
31. Use regression to predict a value of y for a given x.
Division of Mathematics, HCC
Course Objectives for Chapter 11
After studying this chapter, the student will
be able to:
32. Accurately model a situation through
simulation.
33. Discuss the results of a simulation study
and draw conclusions about the
questions being investigated.
Division of Mathematics, HCC
Course Objectives for Chapter 12
After studying this chapter, the student will be able
to:
34. Classify samples, populations, parameters and
statistics.
35. Identify and explain the different sampling
techniques: census, simple random samples,
stratified, cluster, systematic and convenience.
36. Recognize different types of bias.
• Recognize other limitations of sampling.
Division of Mathematics, HCC
Course Objectives for Chapter 13
After studying this chapter, the student will be able to:
37. Recognize the difference between an experiment
and an observational study.
38. Identify observational studies as retrospective
(case-control) or prospective (longitudinal,
cohort) or cross-sectional.
• Explain what a lurking variable is.
• Explain confounding.
• Explain the stages of a clinical trial.
Division of Mathematics, HCC
Course Objectives for Chapter 14
After studying this chapter, the student will be
able to:
39. Apply the Law of Large Numbers.
40. Recognize when events are disjoint and
when events are independent.
41. State the basic definitions and apply the
rules of probability for disjoint and
independent events.
Division of Mathematics, HCC
Course Objectives for Chapter 15
After studying this chapter, the student will be able to:
42. State the definition of sample space, event and
P(A).
43. Apply the General Addition and General
Multiplication rules.
44. Compute conditional probabilities and use the rule
to test for independence.
45. Know how to make and use a tree diagram to
understand conditional probabilities and reverse
conditioning.
Division of Mathematics, HCC
Course Objectives for Chapter 16
After studying this chapter, the student will be able
to:
46. Define random variable and recognize random
variables.
47. Find the probability model for a discrete
random variable.
48. Find and interpret in context the mean
(expected value) and the standard deviation of
a random variable.
Division of Mathematics, HCC
Course Objectives for Chapter 17
After studying this chapter, the student will be able to:
49. Tell if a situation involves Bernoulli trials.
50. Know the appropriate conditions for using a
Binomial or Normal model.
51. Find the mean and standard deviation of a
Binomial model.
52. Calculate binomial probabilities, perhaps with a
Normal model.
• Find the mean and standard deviation of a
Geometric model.
• Calculate and interpret Geometric probabilities.
• Calculate and interpret Poisson probabilities.
Division of Mathematics, HCC
Course Objectives for Chapter 18
After studying this chapter, the student will be
able to:
53. State and apply the conditions and uses of
the Central Limit Theorem.
54. Determine the mean and standard deviation
(standard error) for a sampling distribution of
proportions or means.
55. Apply the sampling distribution of a proportion
or a mean to application problems.
Division of Mathematics, HCC
Course Objectives for Chapter 19
After studying this chapter, the student will be able
to:
56. Construct a confidence interval for a proportion
and interpret the constructed confidence
interval in the context of the problem, checking
the necessary assumptions and conditions.
57. Determine the sample size necessary to
produce a certain margin of error.
• Fully interpret the Gallup poll reported on at the
beginning of this presentation!
Division of Mathematics, HCC
Course Objectives for Chapter 20
After studying this chapter, the student will be able to:
58. Perform a one-proportion z-test, to include:
 writing appropriate hypotheses,
 checking the necessary assumptions and
conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 interpreting the results in the context of the
problem.
Division of Mathematics, HCC
Course Objectives for Chapter 21
After studying this chapter, the student will
be able to:
59. Explain Type I and Type II errors in the
context of the problem.
• Define power and recognize its
importance in statistical inference.
Division of Mathematics, HCC
Course Objectives for Chapter 22
After studying this chapter, the student will be able to:
60. Find a confidence interval for the difference between two
proportions.
– Finding the z that corresponds to the percent
– Computing the interval
– Interpreting the interval in context.
61. Perform a two-proportion z-test, to include:
 writing appropriate hypotheses,
 checking the necessary assumptions and conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 interpreting the results in the context of the problem.
Division of Mathematics, HCC
Course Objectives for Chapter 23
After studying this chapter, the student will be able to:
62. Perform a t-test for the population mean, to include:
 writing appropriate hypotheses,
 checking the necessary assumptions and conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 Interpreting the results in the context of the problem.
63. Find a t-based confidence interval for the population
mean, to include:
– Finding the t that corresponds to the percent
– Computing the interval
– Interpreting the interval in context.
Division of Mathematics, HCC
Course Objectives for Chapter 24
After studying this chapter, the student will be able to:
64. Perform a two-sample t-test for two population means, to
include:
 writing appropriate hypotheses,
 checking the necessary assumptions and conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 Interpreting the results in the context of the problem.
65. Find a t-based confidence interval for the difference
between two population means, to include:
– Finding the t that corresponds to the percent
– Computing the interval
– Interpreting the interval in context.
Division of Mathematics, HCC
Course Objectives for Chapter 25
After studying this chapter, the student will be able to:
66. Find a paired confidence interval, to include:
– Finding the t that corresponds to the percent
– Computing the interval
– Interpreting the interval in context.
67. Perform a paired t-test, to include:
 writing appropriate hypotheses,
 checking the necessary assumptions and conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 interpreting the results in the context of the problem.
Division of Mathematics, HCC
Course Objectives for Chapter 26
After studying this chapter, the student will be able to:
68. Perform chi-square tests for
 goodness-of-fit,
 homogeneity, and
 independence,
to include:
 writing appropriate hypotheses,
 checking the necessary assumptions and conditions,
 drawing an appropriate diagram,
 computing the P-value,
 making a decision, and
 interpreting the results in the context of the problem.