Transcript APStat - Activitiesx - edventure-GA

What Percentage of the Earth’s Surface is
Water?
• Parameter of Interest:
• Procedure:
• Conditions:
• Calculations:
• Conclusion:
Sample Data
Water
Land
Measure The Correlation
For each of the following scatterplots:
• Draw a symmetrical ellipse that characterizes
the data.
• Draw the major and minor axes of the ellipse
• Calculate
 length of the minor axis 
r   1 

length
of
the
major
axis


Randomness and Scrabble
Using the TI-84 to randomly pick a word from a dictionary:
{randint(1, # of pages),
randint(1, # of columns),
randint(1, # of words in column)}
Law of Large Numbers
• Flip an “object” 25 times.
• Record the results in the following table. (Tip
Up – 1, Tip Down – 0)
Trial Number
1
2
3
...
25
Tip Up (1) or Down (0)
Simulating The Central Limit Theorem on the TI-84
• Store 0 in rand
0  rand
[This seeds the random number generator and allows everyone to have the
same population.]
• Create a population.
– Uniform Discrete
randInt (first value, last value, number of values) L1
– Uniform Continuous
First value + Width x rand(number of values)  L1
– Normal
randNorm(mean, standard deviation, number of values)  L1
– Binomial
randBin(number of trials, prob. of a success, number of values)  L1
• Run PGRM CLT
– Population is in L1
– Number of Samples is ___________.
– Sample Size is ___________.
– Your population is stored in LPOP, samples are
temporarily stored in LTEMP, and sample means
are stored in LXBAR.
Determine the characteristics of your sample
means.
• What relationship seems to exist?
• What type of transformation will make this
relationship linear?
Female Mathematicians
A company has 11 mathematicians on its staff,
of who three are women. The president of the
company is concerned about the small number
of women mathematicians. The president learns
that about 40 percent of the mathematicians in
the United States are women, and asks you to
investigate whether or not the number of
women mathematicians in the company is
consistent with the national pool.
Female Mathematicians
• 40 percent of the mathematicians in the
United States are women
– H0: p = .40  A population parameter
• 11 mathematicians on its staff (3 women)
–𝑝=
3
11
 A sample statistic
• The president of the company is concerned!!
Female Mathematicians
• Let’s simulate!
• Using your bag of dice, simulate an 11mathematician company, assuming 40% of the
mathematicians are female.
• Our statistic of interest will be the number of
females.
• Simulate 10 trials and graph your statistics on
the dotplot on the board.
• Determine the p-value.
M&Ms Statistics
Are M&M’s Color Distributions Homogenous?
•
Variable of Interest:
–
•
Parameter of Interest:
–
•
H0: Color Distributions of the different types of M&Ms are the same
Alternative Hypothesis:
–
•
Χ2 Test of Homogeneity
Null Hypothesis:
–
•
Population Distribution of Colors
Test:
–
•
Colors
Ha: Color Distributions of the different types of M&Ms are not the same
Conditions:
–
–
–
•
•
Random Sample – we will assume the company has mixed the colors
Count Data – we are counting the number of M&Ms by color
Expected Counts > 5 - see table
Test Statistic:
(Observed - Expected)2
2  
Expected
Decision Rule:
–
If P-Value < .05, Reject H0
• Sample Data
Color
Brown
Milk
Chocolate
Type
Peanut
Peanut
Butter
• Decision:
Yellow
Red
Blue
Green
Orange
Statistical Inference with Barnum’s
Animal Crackers
• Questions:
– How many types of animals are there?
– How many animals are in a box?
• Null Hypothesis:
• Alternative Hypothesis:
• Test Statistic:
• Conditions:
• Sample Data:
The Runners Population
• Peachtree Road Race 2008 Runners
• Top 2590 Runners
– Rank, Gender Rank, Name, Age, Gender, Home
State (or country if not USA), Time
Sampling
Creating The Sampling Distribution
The CLT Happens
Fathom in Action
1998 FR #1
Benford’s Law
• Benford's Law (which was first mentioned in 1881 by the
astronomer Simon Newcomb) states that if we randomly select a
number from a table of physical constants or statistical data, the
probability of the occurrence of a digit d =
 1
P(d )  log 1  
 d
Deceptive Dice
Quote of the Day
• Robert Mathews, commenting on medical
studies which have a low p-value and thus
are statistically significant but subsequently
turn out to be duds when expanded to the
general population.
“The plain fact is that 70 years ago Ronald
Fisher gave scientists a mathematical
machine for turning baloney into
breakthroughs, and flukes into funding. It is
time to pull the plug.”
Movie Ticket Sales
• Movie box office data sets provide excellent examples of
forecasting features such as trend, seasonality, cycles, and
randomness. The dataset contains both weekend and daily per
theater box office receipts and total US gross receipts for the 49
movies shown. To increase student interest, movies were chosen
from lists of recent Academy Award Best Picture winners, highest
grossing movies, series movies (e.g. the Harry Potter series, the
Spiderman series), and from the Sundance Film Festival.
Normal Probability Plots
•
•
•
•
Sort the data in ascending order
Assign a percentile to each data value
Convert the percentile to a z-score
Plot the z-scores vs. the data
Presidential Days
How long have our presidents been in office?
Cash 3
Select three one-digit numbers (or one 3-digit number).
Purchase your ticket for $1.
If your number matches the chosen number, you win $500.
999
1
 499 
1000
1000
500

 $0.50
1000
On the average for every dollar spent, half is lost.
E[winnings]  1
How do “weird” sample statistics behave?
(The sampling distributions of standard deviation and correlation)
Matching Dogs to Owners
1. Write down the numbers 1-6
2. For each numbered person in the following
photos, write down the letter for the dog that is
owned by that person.
1. _____
A)
2. _____
B)
3. _____
C)
D)
4. _____
5. _____
6. _____
E)
F)
A
1. _____
C
2. _____
F
3. _____
E
4. _____
B
5. _____
D
6. _____