Transcript 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
to login with your UMID.
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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
• We’ve talked about two broad types of
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>0.2)? Choose all that apply...
A) Use sampling distribution of p-hat to find
P(p-hat > 0.2) directly
B) Use normal approximation to binomial to
find P(X > 0.2*n) instead
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
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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
standard errors your observed sample
proportion is from the true proportion.
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