Sampling and Experimental Design
A numerical description of a sample is called a...
A numerical description of a sample is called a statistic.
If rolling two fair 6-sided dice, what is the probability that the sum of their sides is equal to 9?
If rolling two fair 6-sided dice, what is the probability that the sum of their sides is equal to 9?
1/9
Daily Double
What does r measure?
What does r measure?
The strength and direction of a linear relationship.
A student concludes: "The p-value is 0.08, so there is an 8% chance the null hypothesis is true."
What's wrong with this statement?
A student concludes: "The p-value is 0.08, so there is an 8% chance the null hypothesis is true."
What's wrong with this statement?
A p-value is not the probability that H0 is true - it's the probability of obtaining results at least as extreme as those observed assuming H0 is true.
Researchers divide the high school into grades, and randomly sample from each grade, where the sample size is proportion to the total number of students in that grade.
Researchers divide the high school into grades, and randomly sample from each grade, where the sample size is proportion to the total number of students in that grade.
Stratified Random Sample
A fair coin is flipped 6 times. What is the probability of getting exactly 3 heads?
A fair coin is flipped 6 times. What is the probability of getting exactly 3 heads?
5/16 or 31.25%
If r = -0.9, what kind of association exists?
If r = -0.9, what kind of association exists?
Strong, negative, linear association.
Researchers test H0: μ = 50 against Ha: μ > 50 and fail to reject H0. Can they conclude μ = 50? Explain.
Researchers test H0: μ = 50 against Ha: μ > 50 and fail to reject H0. Can they conclude μ = 50? Explain.
No. Failing to reject H0 does not prove H0 is true. It only means there is insufficient evidence for Ha.
Daily Double
A survey about school lunches is emailed to all students, but only students with strong opinions respond. What type of bias is present?
Daily Double
A survey about school lunches is emailed to all students, but only students with strong opinions respond. What type of bias is present?
Voluntary Response Bias
Daily Double!
A random variable X follows the binomial distribution (12, 0.4). Find P(X = 0).
Daily Double!
A random variable X follows the binomial distribution (12, 0.4). Find P(X = 0).
(0.6)12 = 0.0022
A researcher fits a regression model relating study hours (x) to exam score (y). The slope is 4.2. Interpret the slope in context.
A researcher fits a regression model relating study hours (x) to exam score (y). The slope is 4.2. Interpret the slope in context.
For each additional hour studied, the model predicts an increase of about 4.2 points in exam score, on average.
A medical screening test has very low power. Explain what this means in context.
A medical screening test has very low power. Explain what this means in context.
The test has a high probability of failing to reject H0 even when a real effect exists (high chance of Type II error). High probability of detecting a disease/abnormality when one exists.
Researchers want to compare two fertilizers. They randomly assign plants to Fertilizer A or Fertilizer B. What principle of experimental design is being used?
Researchers want to compare two fertilizers. They randomly assign plants to Fertilizer A or Fertilizer B. What principle of experimental design is being used?
Random Assignment
At a school, 60% of students play a sport, 35% are in a club, and 20% do both. A student is selected at random. Given that the student is in a club, what is the probability that they also play a sport?
At a school, 60% of students play a sport, 35% are in a club, and 20% do both. A student is selected at random. Given that the student is in a club, what is the probability that they also play a sport?
P(Sport|Club) = P(Sport and Club) / P(Club) = 0.20/0.35 = 4/7 or ~0.571
A regression model has r2 = 0.64. Interpret this value.
A regression model has r2 = 0.64. Interpret this value.
About 64% of the variability in the response variable is explained by the linear relationship with the explanatory variable.
Daily Double
A researcher lowers the significance level from alpha = 0.05 to alpha = 0.01. How are Type I error probability and power affected?
Daily Double
A researcher lowers the significance level from alpha = 0.05 to alpha = 0.01. How are Type I error probability and power affected?
Type I error probability decreases
Power decreases
A study finds students who sleep more earn higher grades. Can the researchers conclude that more sleep causes higher grades if the study was observational? (why or why not)
A study finds students who sleep more earn higher grades. Can the researchers conclude that more sleep causes higher grades if the study was observational? (why or why not)
No - observational studies can't prove causation (unless they used DAGs, Pearl's Do Calculus, and MCMC?)
A game costs $5 to play. You draw one card from a standard deck. Ace: win $50. Face card: win $10. Any other card: win $0. What is the expected profit for the player?
A game costs $5 to play. You draw one card from a standard deck. Ace: win $50. Face card: win $10. Any other card: win $0. What is the expected profit for the player?
50(4/52)) + 10(12/52) + 0(36/52) = 6.15
6.15 - 5 = $1.15 per game
Daily Double
A dataset has a strong positive linear association. One influential point is removed. After removal:
-The slope changes substantially.
-r increases from 0.7 to
What does this suggest about the removed point?
Daily Double
A dataset has a strong positive linear association. One influential point is removed. After removal:
-The slope changes substantially.
-r increases from 0.7 to
What does this suggest about the removed point?
The point was influential and weakened the linear relationship. It likely had high leverage and did not follow the overall linear pattern.
A test has alpha = 0.05 and power = 0.8. Interpret the power in context.
A test has alpha = 0.05 and power = 0.8. Interpret the power in context.
If the alternative hypothesis is actually true, the test will correctly reject H0 about 80% of the time.