Download Review Exam 1 (Chapter 1-5, 8, 9,10)/Math 1680/Ms

Final Exam Information and Review
Math 1680
Ms. Stonebraker
Math 1680.008 (MWF 11-11:50am):
Date: Friday, May 13
Time: 10:30 a.m. - 12:30 p.m.
Location: WH 221
Special Review Time: Thursday, May 12th (7-9pm) in the Math Lab (GAB 440)
If you made a psuedo-name, your grades will be posted on the website
(http://www.math.unt.edu/~stonebraker) by Saturday morning, May 14th at 8am.
Math 1680.006 (MW 12:30-1:50pm):
Date: Monday, May 9
Time: 10:30 a.m. - 12:30 p.m.
Location: PHYS 104
Special Review Time: Sunday, May 8th (7-9pm) in the Math Lab (GAB 440)
If you made a psuedo-name, your grades will be posted on the website
(http://www.math.unt.edu/~stonebraker) by Wednesday morning, May 11th at 8am.
Special Instructions for the Final Exam:
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Get to the room a little early; there will be a random seating arrangement on the day
of the final.
Bring an ID, pencil, and a calculator.
You will not be able to share calculators.
Your calculator should be able to do a square root function.
Have your phone turned off and out of sight. Do not have your phone on vibrate or
beep. It needs to be completely silent.
Bags should be zipped up.
There are to be no stray papers.
If possible do not bring anything extra.
Review Exam 1 (Chapter 1-5, 8, 9,10)
Study: Quizzes, notes, worksheets, and reread through the book. If you have time, work
through problems in the book again…
Chapter 1 (Controlled Experiments):
 Be able to:
o Define and specifically discuss the importance of the following:

 Controlled experiment
 Control group
 Treatment group
 Double-blind experiment
 Blind experiment
 Randomized study
 Confounding factors
 Self-selected study
o Look at a study and analyze what is right and wrong in regards to its
construction.
o Answer why is it better to compare rates rather than sizes
It is a great idea to look over Quiz 1 and your reading assignment for this chapter.
Chapter 2 (Observational Studies):
 Be able to:
o Discuss random versus observational studies
o Discuss and recognize Simpson’s paradox
o Give example of why association does not necessarily imply causation.
 See Section 3 in this chapter
o Discuss the difference between adherers and non-adherers
Chapter 3 (Histograms);
 Be able to:
o Create a histogram
 Vertical scale is density which is % per horizontal unit
o Create a boxplot (also know as a box-and-whiskers plot)
o Read a histogram
o Recognize a bad histogram
o Discuss and recognize the difference between
 Qualitative and quantitative
 Continuous and discrete
 Density (vertical scale) = percentage / (width of interval)
Chapter 4 (Average and Standard Deviation):
 Be able to:
o Discuss why standard deviation cannot be negative.
o Do word problems associated with averages
o Give an example where the standard deviation is 0
o Give an example where the mean and median are not equal.
 Specifically:
 Mean > median
 Mean < median
o Discuss skewedness
 If skewed right, the mean is larger than the median. Where are the
outliers? What does the graph look like?
 Likewise with skewed left…
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o Discuss when the mean is equal to the median. When is it not?
o Define and/or find the following:
 Median
 Mean
 Q1 – 25th percentile
 Q2 – 50th percentile
 Q3 – 75th percentile
 IQR = Q3 - Q1
 Standard deviation
 RMS
 Outliers
o Recognize what happens to the standard deviation and mean when:
 A number is added to each pieces
 A non-negative number is multiplied by each pieces
 A negative number is multiplied by each pieces
x  x2  ...  xn
Ave(X) = x  1
n
SD =
( x1  x ) 2  ...  ( x n  x ) 2
n
Chapter 5 (The Normal Curve):
This chapter is very important and I would make sure I was very comfortable with what
lies within it.
 Be able to:
o Find a value’s z-score
o Find a z-score’s original value
o Find the percentage above, below, between z-value(s)
o Find a data piece associated with a percentage
o Find a percentage associated with a data piece
o Recall that percentage is cumulative
o Find two data pieces for which there is a certain percentage between those
values when it is centered at the mean
o Make use of a z-chart

z x  SU x 
xx
SD
Chapter 8(Correlation) / Chapter 9 (More about Correlation):
 Be able to:
o Find the correlation coefficient
o Recognize what does not effect the correlation coefficient
 Interchanging the two variables
 Adding the same number to all the values of one variable
 Multiplying all the values of one variable by the same positive
number
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o Know what is means for two things to have a positive or negative
correlation.
o Give and example of something with positive (negative) correlation
o Distinguish if one thing has a stronger correlation then another
o Recognize a graph with a certain mean, standard deviation, and correlation
coefficient
o Recall that r can only be a number between 1 and –1
o Give and graph the equation of a standard deviation line given the mean,
standard deviation, and correlation coefficient
o Know what it means for something to have a certain correlation
coefficient. For example:
 r = .08, weak positive correlation
 r = -.95, strong negative correlation
r  Ave( z x * z y )
SD line equation
 SD(Y ) 
x  Ave( X )   Ave(Y )
o y   
 SD( X ) 
 SD(Y ) 

o Contains the point (Ave(X), Ave (Y)), and has slope of m =  
 SD( X ) 
Chapter 10 (Regression):
 Be able to:
o Give the equation of the regression line
o Graph the equation of the regression line
o Discuss the difference and similarities between the regression and
standard deviation line.
 What point do they have in common?
 How do their slopes differ?
 What does each of the lines try to fit?
o Recognize regression effect and fallacy
o Predict a dependent variable given nothing about the independent variable
o Predict a dependent variable given the correlation coefficient between the
two variable
 Regression Line:
 SD(Y ) 
x  Ave( X )   Ave(Y )
o y  r 
 SD( X ) 
 SD(Y ) 
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o Contains the point (Ave(X), Ave (Y)), and has slope of m = r 
 SD ( X ) 
Review Exam 2 (Chapter 13-18)
Study: Quizzes, notes, and reread through the book starting with the summary portion of
the chapters. If you have time, work through problems in the book again…
Chapter 13 (What are the Chances?) / Chapter 14 (More about Chances):
 Be able to:
o Make use of the multiplication rule
 This rules is associated with ‘and’ statements
o Make use of the addition rule
 This rule is associated with ‘or’ statements
 You can only add two events probabilities if they are mutually
exclusive
o Recognize, discuss, and justify independence and dependence
o Find the probability there is at least one __________
o Find the probability there is no __________
o Make use of compliments
 P(not A) = 1 – P(A)
o Recognize a scenario’s sample space and sample size
 For Example: Roulette has a sample size of 38, and its sample
space is 0, 00, 1, …, 37, and 38.
o Quizzes are a great study guide for this and pretty much all of the sections.
Chapter 15 (Binomial Formula):
 Be able to:
o Recognize when you can and cannot use binomial formula
 To use binomial
 Each time the process is repeated, outcomes can be
classified as either successes or failures
 Each time the process is repeated there is the same
probability of a success occurring
 Successive outcomes are independent of one another
o Recognize when you need to use combination and when you need to use
permutation
o Simplify permutations or combinations
 n
n!
 nCr =   =
…order doesn’t matter
 r  r!(n  r )!
n!
 nPr =
….order is significant
(n  r )!
o Work a problem applying the binomial formula when we are trying to find
the probability of having
 Exactly a certain amount of successes
 More than a certain amount of successes
 Less than a certain amount of successes
 At least a certain amount of successes
 No more than a certain amount of successes
 n
n!
nr
nr
p r 1  p 
   p r 1  p  
r
r!n  r !
 
Chapter 16 (The Law of Averages):
 Be able to:
o Apply the law of averages
o Recognize when the law of averages is in favor of a certain event or not
o Find absolute chance error and relative chance error given a scenario
o Set up a box model for an independent chance process
o Recognize how many draw will be needed from the box
Chapter 17 (The Expected Value and Standard Error):
This section is important. Pay close attention and be able to work out what lies within.
 Be able to:
o EVBOX is the average of a box model
o EVSUM = EVBOX  N
o SDBOX = (BIG – SMALL) PBIG  PSMALL
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o
o
o
o
o
o
This is the short cut method and only applies when there are only
two types of tickets in the box
SE = SDSUM = SDBOX  N
Recognize that the sum is likely to be around the EVSUM give or take the
SE or so.
Use these values to standardize a sum
Use the normal chart to determine the probability that your sum is less
than, more than, or between certain values.
Remember when you can and cannot use normal approximation
 You have to use binomial if the number of draws are less than 30
Use a box model to evaluate the sum of draws to find
 Net Gain/loss
 This answers the question “how much…?”
 You use the amount you win and lose to construct the box
model
 Count the number of times an event occurred
 This answers the question “how many …?”
 You use 0’s and 1’s to construct this model
Chapter 18 (The Normal Approximation for Probability Histograms):
 Be able to:
o Read a histogram and discuss how the bars represent probabilities
o Discuss and apply the central limit theorem
o Discuss what an empirical histogram is and when it starts to follow the
expected probability histogram
Chapter 19, 20, 21, and 23
Chapter 19 (Sample Surveys)
Be able to:
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Define and discuss the following terms:
o Population
o Parameter
o Sample
o Statistic
o Quota sampling
o Simple random sampling
o Multi-stage cluster sampling
Recognize errors with a sample survey
Recall that all sample surveys have chance error and bias
Recall the four questions that one should ask when examining a sample survey
o What is the population?
o What is the parameter being estimated?
o How was the sample chosen?
o What was the response rate?
Chapter 20 (Chance Errors in Sampling)
Be able to:
 Discuss what the central limit theorem tell us about averages
EVBOX
o EVAVE = EVBOX =
n
SD BOX SDSUM
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o SEAVE =
n
n
 Use the previous equations to predict the make up of a sample given information
regarding the sample.
 Recall the accuracy of the sample percentage is determined by the absolute size of
the sample, not the size relative to the population.
 Recall that if the sample is selected from the population without replacement and
the sample is large with respect to the population, then a correction factor is
needed for the standard error.
o I am not going to ask you to memorize the equation for the correction
factor, but you need to recognize when a correction factor is needed.
Chapter 21 (The Accuracy of Percentages):
Be able to:
 Recognize when a confidence interval is appropriate and when it is not
 Find a confidence interval
 Explain what a confidence interval tells predicts
 Discuss the differences between SD and SE
Chapter 23 (The Accuracy of Averages):
Be able to:
 Find confidence intervals when working with averages as opposed to percentages.
 See chapter 20 for EV and SE equations for averages.