Experiments + Sampling
What is the only way to prove cause and effect?
Run an experiment!
Name at least 3 things you must describe when you hear: "Describe the distribution"
Shape
Outliers
Center
Context
Spread
Name at least 3 things you must describe when you hear: "Describe the relationship"
Form
Outliers
Context
Slope/direction
Strength
What strategy would you use for successive dependent events?
Draw a tree diagram
X = $ amount for each size soda
Meanx = 1.8
SDx = .7
Find the new mean and sd if the store increases their prices of soda by $2 each
Meanx+2 = 3.8
SDx+2 = .7
Name a benefit of stratified random sampling over simple random sampling
Stratifying is more precise
Stratifying ensures representation from the entire population, whereas an SRS may miss parts of the population by chance
Name a representation you would use for 1-variable quantitative data
Possible answers:
- Histogram
- Dot Plot
- Stem Plot
Name a representation you would use for 2-variable quantitative data
Scatterplot
Given that P(A) = 0.6 and P(B) = 0.3 and P(B|A) = 0.5
(a) What is P(A and B)?
(b) What is P(A or B)?
(c) Are events A and B independent?
a) P(A and B) = (.3)(.5) = .15
b) P(A or B) = .3+.5-.15 = .65
c) No, because P(B) is not = to P(B|A)
Suppose a supermarket hands out coupons randomly to its customers. Consider the probability that a customer receives a certain number of gift cards in a given week. Define the random variable of interest, C
C = The number of coupons a customer gets in a given week
Random sampling eliminates...?
Random assignment eliminates...?
Bias
Confounding factors
If the data is skewed right, what does this mean about the location of the mean versus the median?
The mean is to the right of the median.
Interpret the SLOPE and Y-INTERCEPT in context:
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model
ŷ = 25.2 + 3.3x
where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit.
Slope: For every 1 chirp per minute, our model predicts that the temperature will increase by 3.3 degrees Fahrenheit
Y-Int: When there are 0 chirps made by ground crickets, the temperature is predicted to be 25.2 degrees.
What is the strategy for "at least one"?
1 - P(None)
Roll a six-sided die,
If ≤ 2, win $10
If > 5, win $20
10(2/6) + 20(1/6)
20/6 + 20/6 = 40/6 = 6.67
In order to perform an experiment using 60 members of a gym, I first divide the list of members into men and women because I feel that the results will be different based on gender. I then randomly choose 30 men and 30 women. I assign half of the men to the treatment group and half to the control group. I repeat this procedure with the women. This is an example of a:
Blocked Experimental Design
Describe a process for identifying outliers
Identify Q1 and Q3 by first finding the median, then find the median of the lower half of the data (Q1) and the median of the upper half of the data (Q3).
Calculate IQR by taking Q3-Q1
Identify outliers by finding the lower and upper limits given by: Lower = Q1-(1.5*IQR), Upper=Q3+(1.5*IQR)
If there is a number outside the limits, it is an outlier.
Consider the following data on population of a small town recorded from 1995 to 2000.
Year: 1995, 1996, 1997, 1998, 1999, 2000
Pop: 1300, 1250, 1250, 1150, 1000, 950
What is the equation of the least squares regression line?
ŷ = -74.29X + 149535.71
The probability someone makes an 5 in AP statistics test is .15. Ms. Bassell teaches 60 students. What is the probability at least 6 students make a 5?
.903
What are the requirements for the distribution of a random variable to be geometric or binomial?
Binary, independent trials
A dermatologist will conduct an experiment to investigate the effectiveness of a new drug to treat acne. The dermatologist has recruited 36 pairs of identical twins. Each person in the experiment has acne and each person in the experiment will receive either the new drug or a placebo. After each person in the experiment uses either the new drug or the placebo for 2 weeks, the dermatologist will evaluate the improvement in acne severity for each person on a scale from 0 (no improvement) to 100 (complete cure)
Describe how to implement a matched pairs design.
For each pair of twins, label one person as twin A and label the other person as twin B. For each pair of twins, toss a coin. If the coin lands on heads, twin A gets the placebo and twin B gets the active drug. If the coin lands on tails, twin A gets the active drug and twin B gets the placebo.
(Something akin to this response)
In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height to be in the top 22%.
71.92 inches
The coefficient of determination between the length (x) in inches and the weight (y) in pounds of a sample of brook trout is 0.78.
Interpret this number.
78% of the variation in length of brook trout can be explained by the linear relationship with weight
The probability you find a defective bag of popcorn is .02. What is the probability that you will find the first defective bag after the 10th bag?
.817
Let U and V be random variables that are approximately normally distributed.
MeanU = 500, SDU = 15
MeanV = 200, SDV = 8
Let T = U + V
Find P(T > 717)
MeanT = 500 + 200 = 700
SDT = √(152+82) = 15.30
P(T>717) = normalcdf(700, 15.30, 717, 10000) = 0.1333