Monday, October 14

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Monday, October 14 Statistical Inference and
Probability
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Population
Sample
You take a sample.
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High Stakes Coin Flip
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High Stakes Coin Flip
Could your professor be a crook?
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High Stakes Coin Flip
Could your professor be a crook?
Lets do an experiment.
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The Coin Flip Experiment

• Question Could the professor be a crook?
• Lets do an experiment.
• Make assumptions about the professor.
• Determine sampling frame.
• Set up hypotheses based on assumptions.
• Collect data.
• Analyze data.
• Make decision whether he is or is not a crook.

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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook.
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook. Step 3. Determine
the risk that you are willing to take in making
an error of false slander, ? (alpha), often at
.05
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook. Step 3. Determine
the risk that you are willing to take in making
an error of false slander, ? (alpha), often at
.05 Step 4. Decide on a sample, e.g., 6 flips.
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook. Step 3. Determine
the risk that you are willing to take in making
an error of false slander, ? (alpha), often at
.05 Step 4. Decide on a sample, e.g., 6
flips. Step 5. Gather data.
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook. Step 3. Determine
the risk that you are willing to take in making
an error of false slander, ? (alpha), often at
.05 Step 4. Decide on a sample, e.g., 6
flips. Step 5. Gather data. Step 6. Decide
whether the data is more or less probable than ?
. E.g., the probability of 6 consecutive wins
based on the assumption in Step 1 is .016. (.5 x
.5 x .5 x .5 x .5 x .5 .016)
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Some Steps in Hypothesis Testing Step 1. Assume
that the professor is fair, i.e., that P(Win)
.5 Step 2. Set up hypotheses H0 He is not a
crook. H1 He is a crook. Step 3. Determine
the risk that you are willing to take in making
an error of false slander, ? (alpha), often at
.05 Step 4. Decide on a sample, e.g., 6
flips. Step 5. Gather data. Step 6. Decide
whether the data is more or less probable than ?
. E.g., the probability of 6 consecutive wins
based on the assumption in Step 1 is .016. (.5 x
.5 x .5 x .5 x .5 x .5 .016) Step 7. Based on
this evidence, determine if the assumption that
Hakuta is fair should be rejected or not.
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Whats the probability of rolling a dice and
getting 6?
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Whats the probability of rolling a dice and
getting an even number?
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What the probability that your first (or next)
child will be a girl?
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Its a girl!
1/2 .50
2 possible outcomes (boy or girl)
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What the probability that your first (or next)
child will be a girl and when she makes her
first roll of dice, rolls an even number?
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P(girl) ? P(even)
.5 x .5 .25
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What the probability that your first (or next)
child will be a girl or when that child makes
his/her first roll of dice, rolls an even number?
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What the probability that your first (or next)
child will be a girl or when that child makes
his/her first roll of dice, rolls an even number?
List the possible outcomes.
Girl, rolls even. Girl, rolls odd. Boy, rolls
even. Boy, rolls odd.
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What the probability that your first (or next)
child will be a girl or when that child makes
his/her first roll of dice, rolls an even number?
List the possible outcomes.
? Girl, rolls even. ? Girl, rolls odd. ? Boy,
rolls even. ? Boy, rolls odd.
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What the probability that your first (or next)
child will be a girl or when that child makes
his/her first roll of dice, rolls an even number?
List the possible outcomes.
.25 .25 .25 .25
? Girl, rolls even. ? Girl, rolls odd. ? Boy,
rolls even. ? Boy, rolls odd.
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What the probability that your first (or next)
child will be a girl or when that child makes
his/her first roll of dice, rolls an even number?
List the possible outcomes.
.25 ? .25 ? .25 ? .25
? Girl, rolls even. ? Girl, rolls odd. ? Boy,
rolls even. ? Boy, rolls odd.
.75
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Addition Rule of Probabilities
P(A?B) P(A) P(B) - P(A?B)
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Addition Rule of Probabilities
P(A?B) P(A) P(B) - P(A?B)
P (A) P(girl) .5 P (B) P (even) .5 P
(A?B) P(A) x P(B) .25
P(A?B) .5 .5 - .25 .75
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Addition Rule of Probabilities
P(A?B) P(A) P(B) - P(A?B)
P (A) P(girl) .5 P (B) P (even) .5 P
(A?B) P(A) x P(B) .25
P(A?B) .5 .5 - .25 .75
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What is the probability of flipping 8 heads in a
row?
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What is the probability of flipping 8 heads in a
row?
.5 x .5 x .5 x .5 x .5 x .5 x .5 x .5 or .58
.004
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What is the probability of flipping 8 heads in a
row?
.5 x .5 x .5 x .5 x .5 x .5 x .5 x .5 or .58
.004
Formalized as The probability that A, which has
probability P(A), will occur r times in r
independent trials is
P(A)r
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So, you decide to conduct a case study of 3
teachers, sampling randomly from a school
district where 85 of the teacher are women. You
end up with 3 male teachers. What do you
conclude?
P(males) three times P(males)3 .153 .003
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So, you decide to conduct a case study of 3
teachers, sampling randomly from a school
district where 85 of the teacher are women. You
end up with 3 male teachers. What do you
conclude?
P(males) three times P(males)3 .153 .003
If you had ended up with 3 female teachers,
would you have been surprised?
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