Statistics Exam #3 Study Guide Flashcards

Practice vocabulary flashcards covering key statistical concepts, probability rules, distributions, and inferential testing based on the Exam #3 study guide.

Statistic

A numerical summary that describes a characteristic of a sample.

Population

The entire group of individuals or objects about which the researcher wants to draw conclusions.

Parameter

A numerical summary that describes a characteristic of the population, such as the average height of all adult males in the United States.

Experimental Study

A study where researchers randomly assign participants to receive different treatments (e.g., a daily supplement vs. a placebo) to compare outcomes.

Convenience Sample

A non-random sampling method (e.g., using students from a single department) that limits the generalizability of findings to the larger population.

Observational Study

A study where no treatment is imposed and researchers observe subjects; it can identify correlations but cannot rule out lurking variables.

Explanatory Variable

The variable in a study that is used to explain or predict changes in the response variable (e.g., the amount of fertilizer applied).

Response Variable

The outcome variable that is measured in a study (e.g., the height of a plant or a patient's reported pain level).

Control Group / Placebo

A group used to provide a baseline for comparison, accounting for the placebo effect or other confounding factors.

Relationship of Mean and Median (Left Skewed)

In a distribution that is left skewed, the median is likely to be greater than the mean.

Median

The measure of center that is most resistant to the influence of extreme outliers.

Standard Deviation ($s$)

A value representing the typical or average distance of the data points from the mean.

Disjoint (Mutually Exclusive)

A term describing two events that cannot happen at the same time.

Independent Events

Events where the occurrence of one does not affect the probability of the other; the probability of both occurring is $P(A) \times P(B)$.

Complementary Event ($A^c$)

An event defined by drawing or selecting any outcome that is not part of original Event A.

Union (A or B)

The set of outcomes that belong to event A, or event B, or both.

Intersection (A and B)

The set of outcomes that belong exclusively to both event A and event B.

Conditional Probability

A probability based on a specific outcome having already occurred, such as $P(\text{Defective} \mid \text{Machine A})$.

Discrete Random Variable

A variable with countable outcomes, such as the number of heads resulting from 10 coin flips.

Continuous Random Variable

A variable that can take on any value within a given range of values.

$P(X=c)$ (Continuous Variable)

The probability that a continuous random variable takes on an exact single value is always zero.

Area Under the Probability Curve

The mathematical concept used to determine the probability for a continuous random variable, such as P(20 < X < 30).

Normal Random Variable

A random variable characterized by a symmetric and bell-shaped distribution defined by its mean $\mu$ and standard deviation $\sigma$.

Z-score ($z$)

A numerical value representing how many standard deviations a data value is above or below the mean.

Binomial Random Variable conditions

1. Fixed number of trials ($n$). 2. Independent trials. 3. Two possible outcomes (success/failure). 4. Constant probability of success ($p$).

Sampling Variation

The natural, random differences in statistics calculated from different samples drawn from the same population.

Standard Error

The standard deviation of the sampling distribution of a sample statistic.

Confidence Interval

A plausible range of values calculated from a sample that is likely to contain the true population parameter.

Confidence Level

The long-run proportion of similarly constructed confidence intervals that contain the true population parameter.

Margin of Error

The maximum expected difference between the point estimate and the true population parameter for a given confidence level.

Hypothesis Testing

The process of evaluating two competing, mutually exclusive claims about a population parameter using sample evidence.

P-value

The probability of observing a sample statistic as extreme as (or more extreme than) the one observed, assuming the null hypothesis ($H_0$) is true.

Type I Error

An error that occurs when a researcher rejects a true null hypothesis.

Null Hypothesis ($H_0$)

The crucial assumption made at the beginning of the hypothesis testing process that the base claim is true.

Chi-Square Test for Goodness of Fit

A test used to assess whether the observed counts of a single categorical variable follow a claimed or expected distribution.

t-distribution

A distribution that is wider and shorter than the standard normal ($z$) distribution, reflecting greater uncertainty, especially with smaller sample sizes.

t-test for Paired Means

A test used to determine significant change when measurements are taken before and after a treatment on the same subjects (dependent samples).

ANOVA (Analysis of Variance)

A method used to determine if the means of three or more independent populations are equal.

Correlation Coefficient ($r$)

A value (between -1 and 1) that describes the strength and direction of a linear relationship between two variables.

Regression Slope

The predicted change in the response variable ($Y$) for every one-unit increase in the explanatory variable ($X$).

Coefficient of Determination ($R^2$)

The percentage of the total variation in the response variable ($Y$) that is explained by the variation in the explanatory variable ($X$) within the model.

Residual

The difference between the actual observed value of the response variable ($Y$) and the value predicted by the regression line.

Least Squares Line

The unique line that minimizes the sum of the squared vertical distances (residuals) from the observed data points to the line.

Y-intercept Interpretation

The predicted price or value for a subject when the explanatory variable ($X$) is zero; often meaningless if zero is outside the scope of the data.