Probability & Predictions
In probability theory, if the occurrence of Event A has absolutely no effect on the probability of Event B occurring, the two events are said to have this relationship.
What are Independent Events?
The entire group or set of individuals you want to study or draw conclusions about is....
What is Population?
The median of this dataset: 3, 9, 4, 11, 5
What is 5?
When conducting a hypothesis test, this is the specific name given to the default claim that there is "no effect" or "no difference."
What is Null Hypothesis?
If the correlation coefficient (r) between ice cream sales and sunscreen sales is 0.92, it indicates this type of relationship strength and direction.
What is a strong positive relationship?
The probability of Abraham flipping a fair coin and getting heads 4 times in a row.
What is 1/16? (or 0.0625 / 6.25%)
A smaller, manageable portion of the population selected for a study is....
What is a Sample?
If a dataset has a mean of 50 and a standard deviation of 5, this is the Z-score of a data point with a value of 62.
What is 2.4? (62-50 / 5)
This error occurs if a researcher rejects the null hypothesis when it is actually true (a false positive)
What is a Type I Error?
In a simple linear regression equation (Y Hat) = 3x + 5, this is the predicted value of y when x is equal to 4.
What is 17? (3(4) + 5 = 17)
In a standard deck of 52 cards, what is the probability of Jayden Grant drawing either a King or a Heart.
(There are thirteen hearts , four kings, four queens, two jokers in a standard deck)
What is 17/52 ?
Any characteristic or property that can take on different values (e.g., age, height, test scores) is...
What is a Variable?
In a data set with a minimum of 12, a first quartile (Q1) of 20, a median of 25, a third quartile (Q3) of 32, and a maximum of 50, any value above this number is considered a statistical outlier.
What is 50? (The outlier boundary is Q3 + 1.5(IQR), which is 32 + 18 = 50. Any value strictly greater than 50 is an outlier.)
If a researcher sets their significance level (alpha) at 0.05, and their test yields a p-value of 0.02, they should make this final decision regarding the null hypothesis.
What is Reject the Null Hypothesis? (Because the p-value is less than alpha.)
If the coefficient of determination (R^2) for a regression model predicting test scores based on study hours is 0.64, this is the percentage of the variation in test scores explained by study hours.
What is 64%?
If Janice rolls two standard six-sided dice, this is the most likely sum she will get.
(There are 36 possible outcomes when rolling two standard six-sided dice how many ways can you roll a seven)
What is 7? (there are 6 ways to roll a seven)
The actual collected observations, measurements, or responses is....
What is Data?
If the variance of a sample is 64, this is its standard deviation
What is 8? (The standard deviation is the square root of the variance.)
This term describes the number of independent values or quantities that can vary in a statistical calculation, often calculated as n - 1 for a simple t-test.
What are Degrees of Freedom?
In a linear regression model, this term refers to the vertical distance between an actual observed data point and the regression line's predicted value (essentially, the prediction error)
What is a residual?
If Leuris is guessing blindly on a 5-question, multiple-choice quiz where each question has 4 options, this is the probability of him getting a perfect score.
What is 1/1024 (or about 0.098%)? (Calculated as (1/4)^5
(he is NOT passing this test)
A data point that is significantly different or distant from the rest of the observations in a dataset is....
What is an Outlier?
If a population has a standard deviation of 20 and you take a random sample of 100 individuals, this is the standard error of the sample mean.
What is 2? (20/square root of 100 = 20/10= 2)
In a scatterplot, if all the data points fall perfectly on a straight line that slopes downward from left to right, the correlation coefficient (r) between the two variables would be exactly this number
What is -1?
If two variables have a correlation coefficient (r) of exactly 0, it means there is absolutely none of this specific type of relationship between them.
What is a linear relationship?