# Data - Statistics ```Stat 350 Lab Session
GSI: Yizao Wang
Section 016 Mon 2pm30-4pm MH 444-D
Section 043 Wed 2pm30-4pm MH 444-B
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Outline
• First midterm exam reminder
• Big ideas review
• Qwizdom and non-qwizdom review
questions
• In lab project (ILP) on proportion
Today’s Qwizdom question is anonymous, you don’t have
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First Midterm Exam
• 14th Feb. 6pm-7pm30 1324 EH
• Material:
Ch. 1, 2, 3, 4, 7, 8, 9.1-9.4, 10.1-10.3, 12.1-12.3, 12.5
HW 1-4 and all lab material
• Bring: PICTURE ID, Pen/pencils, erasers, and a
calculator. Formula cards with tables will be provided
with the exam.
• Alternate, randomized seating will be used in the exam rooms.
• No cell phones, beepers, palm pilots allowed in the exam rooms.
• All bags/backpacks will be placed against the exam room wall, so
the less extra things you bring, the better.
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Data
data this semester
• Do you remember what they are?
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Probability
• We learned several rules for calculating
probabilities of events
– E.g. the event ‘Tails’ in the flip of a fair coin
• Special relationships between two events
– Mutually exclusive
– Independent
– Could you provide definitions and examples of
each?
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Random Variables
• We’ve talked about two types of random
variables
– Can you name them?
• We’ve talked about three different models
(i.e. distributions) for random variables
– Can you describe them (be specific)?
– Can you find probabilities under each?
– Do you know which model is appropriate for
each type?
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Sampling Distribution of p-hat
• Can you describe what the sampling
distribution of p-hat is?
• Do you know when to use it?
– When the problem asks you to find a
probability for a sample proportion
– When the sample size is large enough:
np≥10, n(1-p) ≥10
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Confidence Intervals for p
• Useful when we want to provide a range of
reasonable estimates for the population
proportion
• Do you know how to interpret the
confidence level?
• Do you know how to use a confidence
interval to make a decision, and under
what conditions this would be appropriate?
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Hypothesis Testing for p
• Useful for making a Yes/No type decision
about particular value(s) of a population
proportion
• Do you know the 5 steps of hypothesis
testing?
• Can you interpret and calculate a test
statistic?
• Can you interpret and calculate a p-value?
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If your p-value is significant at the 5% level,
then it will also be significant at the …
A)
B)
C)
D)
1% level
10% level
Both of the above
None of the above
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True or False
The standard error of p-hat estimates,
roughly, the average distance of an
observed p-hat value from the true
population proportion.
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I tell you “A and B are mutually exclusive.”
Choose all of the true statements below.
A)
B)
C)
D)
E)
A and B are independent
P(A and B) = 0
P(A and B) = P(A)P(B)
P(A or B) = P(A) + P(B)
None of the above are true
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X has the Bin(n,p) distribution. How would you
find P(p-hat&gt;0.2)? Choose all that apply...
A) Use sampling distribution of p-hat to find
P(p-hat &gt; 0.2) directly
B) Use normal approximation to binomial to
C) Not enough information
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Which of the following distributions for X meet
the criteria to use the normal approximation?
Choose all that apply...
Binomial(25, 0.2)
Binomial(25, 0.5)
Binomial(25, 0.7)
None of the above
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Which graph(s) would be appropriate to display
a quantitative variable? Choose all that apply...
Bar chart
Histogram
Boxplot
QQ-plot
Time-series plot
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Which graph(s) would be appropriate to display
shape of a distribution? Choose all that apply...
Histogram
Boxplot
QQ-plot
Time-series plot
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A well constructed survey of monkeys found
that 75% of monkeys with prehensile tails
prefer bananas to grubs.
Express this as a conditional probability.
P(prehensile tail | prefer bananas) = 0.75
P(prefer bananas | prehensile tail) = 0.75
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To determine if monkey tail status (prehensile
or not) is independent of food preference
(bananas or grubs), we could compare
P(prefer bananas | prehensile tail) to…
P(prehensile tail | prefer bananas)
P(prehensile tail)
P(prefer bananas)
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A 95% confidence interval will be ________ a
99% confidence interval.
Narrower than
Wider than
The same as
Can’t tell
19
Match the type of random variable
to the appropriate distribution(s)
1. Discrete
a. Normal(μ,σ)
2. Continuous
b. Uniform(a,b)
c. Binomial(n,p)
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True or False
A z-statistic tells you how many