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AP Statistics Review Final Exam Review
Questions with Answers.
Addition Rule - Answer>> P(A ∪ B) = P(A) + P(A) - P(A ∩ B) aids in computing the chances of one of several events occurring at a given time. Alpha (α) - Answer>> The probability of a Type I error. See significance level. Alternative Hypothesis - Answer>> The hypothesis stating what the researcher is seeking evidence of. A statement of inequality. It can be written looking for the difference or change in one direction from the null hypothesis or both. Association - Answer>> Relationship between or among variables. Back-Transform - Answer>> The process by which values are substituted into a model of transformed data, and then reversing the transforming process to obtain the predicted value or model for nontransformed data. Bar Chart - Answer>> A graphical display used with categorical data, where frequencies for each category are shown in vertical bars. Bell-Shaped - Answer>> Often used to describe the normal distribution. See mound-shaped.
Beta (β) - Answer>> The probability of a Type II error. See power. Bias - Answer>> The term for systematic deviation from the truth (parameter), caused by systematically favoring some outcomes over others. Biased - Answer>> A sampling method is biased if it tends to produce samples that do not represent the population. Bimodal - Answer>> A distribution with two clear peaks. Binomial Distribution - Answer>> The probability distribution of a binomial random variable. Binomial Random Variable - Answer>> A random variable x (a) that has a fixed number of trials of a random phenomenon n, (b) that has only two possible outcomes on each trial, (c) for which the probability of a success is constant for each trial, and (d) for which each trial is independent of other trials. Bins - Answer>> The intervals that define the "bars" of a histrogram. Bivariate Data - Answer>> Consists of two variables, an explanatory and a response variable, usually quantitative.
Clusters - Answer>> Heterogeneous subgroups of a population. Coefficient of Determination (r²) - Answer>> Percent of variation in the response variable explained by its linear relationship with the explanatory variable. Complement - Answer>> The compliment of an event is that event not occurring. Complementary Randomized Design - Answer>> One in which all experimental units are assigned treatments solely by chance. Conditional Distribution - Answer>> See conditional frequencies. Conditional Frequencies - Answer>> Relative frequencies for each cell in a two-way table relative to one variable. Conditional Probability - Answer>> The probability of an event occurring given that another has occurred. The probability of A given that B has occurred is denoted as P(A|B). Confidence Intervals - Answer>> Give an estimated range that is likely to contain an unknown population parameter.
Confidence Level - Answer>> The level of certainty that a population parameter exists in the calculated confidence interval. Confounding - Answer>> The situation where the effects of two or more explanatory variables on the response variable cannot be separated. Confounding Variable - Answer>> A variable whose effect on the response variable cannot be untangled from the effects of the treatment. Contingency Table - Answer>> See two-way table. Continuous Random Variables - Answer>> Those typically found by measuring, such as heights or temperatures. Control Group - Answer>> A baseline group that may be given no treatment, a faux treatment like a placebo, or an accepted treatment that is to be compared to another. Control - Answer>> The principle that potential sources of variation due to variables not under consideration must be reduced. Convenience Sample - Answer>> Composed of individuals who are easily accessed or contacted. Correlation Coefficient (r) - Answer>> A measure of the strength of a linear relationship,
Double-Blind - Answer>> When both the subjects and data gatherers are ignorant about which treatment a subject received. Empirical Rule (68-95-99.7) Rule - Answer>> Gives benchmarks for understanding how probability is distributed under a normal curve. In the normal distribution, 68% of the observations are within one standard deviation of the mean, 95% is within two standard deviations of the mean, and 99.7% is within three standard deviations of the mean. Estimation - Answer>> The process of determining the value of a population parameter from a sample statistic. Expected Value - Answer>> The mean of a probability distribution. Experiment - Answer>> A study where the researcher deliberately influences individuals by imposing conditions and determining the individuals' responses to those conditions. Experimental Units - Answer>> Individuals (a person, a plot of land, a machine, or any single material unit) in an experiment. Explanatory Variable - Answer>> Explains the response variable, sometimes known as the treatment variable.
Exponential Model - Answer>> A model of the form y = abˣ. Extrapolation - Answer>> Using a model to predict values far outside the range of the explanatory variable, which is prone to creating unreasonable predictions. Factors - Answer>> One or more explanatory variables in an experiment. First Quartile - Answer>> Symbolized Q1, represents the median of the lower 50% of a data set. Five-Number Summary - Answer>> The minimum, first quartile (Q1), median, third quartile (Q3), and maximum values in a data set. Frequency Table - Answer>> A display organizing categorical or numerical data and how often each occurs. Geometric Distribution - Answer>> The probability distribution of a geometric random variable X. All possible outcomes of X before the first success is seen and their associated probabilities. Geometric Random Variable - Answer>> A random variable X (a) that has two possible outcomes of each trial, (b) for which the probability of a success is constant for each trial, and (c) for which each trial is independent of the other trials.
relative frequency as the number of traits of random phenomenon increases. Least-Squares Regression Line (LSRL) - Answer>> The "best-fit" line that is calculated by minimizing the sum of the squares of the differences between the observed and predicted values of the line. The LSRL has the equation ŷ = bo + b1x. levels - Answer>> The different quantities or categories of a factor in an experiment. Linear Regression - Answer>> A method of finding the best model for a linear relationship between the explanatory and response variable. Logarithmic Transformation - Answer>> Procedure that changes a variable by taking the logarithm of each of its values. Lurking Variable - Answer>> A variable that has an effect on the outcome of a study but was not part of the investigation. margin of Error - Answer>> A range of values to the left and right of a point estimate. Marginal Distribution - Answer>> See marginal frequencies.
marginal Frequencies - Answer>> Row totals and column totals in a two-way table. Matched-Pairs Design - Answer>> The design of a study where experimental units are naturally paired by a common characteristic, or with themselves in a before- after type of study. Maximum - Answer>> The largest numerical value in a data set. Mean - Answer>> The arithmetic average of a data set; the sum of all the values divided by the number of values, x̄ = (Σxi)/n. Mean of a Binomial Random Variable X - Answer>> μx = np. Mean of a Discrete Random Variable - Answer>> μx = Σ from i=1 to n of xiP(xi). Mean of a Geometric Random Variable - Answer>> μx=1/p. measures of Center - Answer>> These locate the middle of a distribution. The mean and median are measures of center. Median - Answer>> The middle value of a data set; the equal areas point, where 50% of the data are at or below this value, and 50% of the data are at or above this value.
Observational Study - Answer>> Attempts to determine relationships between variables, but the researcher imposes no conditions as in an experiment. Observed Values - Answer>> Actual outcomes or data from a study or an experiment. One-Way Table - Answer>> A frequency table of one variable. Outlier - Answer>> An extreme value in a data set. Quantified by being less than Q1 - 1.5IQR or more than Q3 + 1.5IRQ. Percentiles - Answer>> Divide the data set into 100 equal parts. An observation at the Pth percentile is higher tha P percent of all observations. Placebo - Answer>> A faux treatment given in an experiment that resembles the real treatment under consideration. Placebo Effect - Answer>> A phenomenon where subjects show a response to a treatment merely because the treatment is imposed regardless of its actual effect. Point Estimate - Answer>> An approximate value that has been calculated for the unknown parameter.
Population - Answer>> The collection of all individuals under consideration in a study. Population Parameter - Answer>> A characteristic or measure of a population. Position - Answer>> Location of a data value relative to the population Power - Answer>> The probability of correctly rejecting the null hypothesis when it is in fact false. Equal to 1 - β. See beta and Type II error. Power Model - Answer>> A function in the form of y - axᵇ. Predicted Value - Answer>> The value of the response variable predicted by a model for a given explanatory variable. Probability - Answer>> Describes the chance that a certain outcome of a random phenomenon will occur. Probability Distribution - Answer>> A discrete random variable X is a function of all n possible outcomes of the random variable (xi) and their associated probabilities P(xi). Probability Sample - Answer>> Composed of individuals selected by chance.
Relative Frequency - Answer>> Percentage or proportion of the whole number of data. Replication - Answer>> The practice of reducing chance variation by assigning each treatment to many experimental units. Residual - Answer>> Observed value minus predicted value of the response variable. Response Bias - Answer>> Because of the manner in which an interview is conducted, because of the phrasing of questions, or because of the attitude of the respondent, inaccurate data are collected. Response Variable - Answer>> Measures the outcomes that have been observed. Sample - Answer>> A selected subset of a population from which data are gathered. Sample Statistic - Answer>> Result of a sample used to estimate a parameter. Sample Survey - Answer>> A study that collects information from a sample of a population in order to determine one or more characteristics of the population.
Sampling Distribution - Answer>> The probability distribution of a sample statistic when a sample is drawn from a population. Sampling Distribution of the Sample Mean (x̄) - Answer>> The distribution of sample means from all possible simple random samples of size n taken from a population. Sampling Distribution of a Sample Proportion p̂ - Answer>> The distribution of sample proportions from all possible simple random samples of size n taken from a population. Sampling Error - Answer>> See sampling variability. Sampling Variability - Answer>> Natural variability due to the sampling process. Each possible random sample from a population will generate a different sample statistic. Scatterplots - Answer>> Used to visualize bivariate data. The explanatory variable is shown on the horizontal axis and the response variable is shown on the vertical axis. Significance Level - Answer>> The probability of a Type I error. A benchmark against which the P-value compared to determine if the null hypothesis will be rejected. See also alpha. Simple Random Sample (SRS) - Answer>> A sample where n individuals are selected from a population in a
z = (observation - mean) / (standard deviation). Statistically Significant - Answer>> When a sample statistic is shown to be far from a hypothesized parameter. When the P-value is less than the significance level. Stemplot - Answer>> Also called a stem-and-leaf plot. Data are separated into a stem and leaf by place value and organized in the form of a histogram. Strata - Answer>> Subgroups of a population that are similar or homogeneous. Stratification - Answer>> Part of the sampling process where units of the study are separated into strata. Stratified Random Sample - Answer>> A sample in which simple random samples are selected from each of several homogeneous subgroups of the population, known as strata. Subjects - Answer>> individuals in an experiment that are people. Symmetric - Answer>> The distribution that resembles a mirror image on either side of the center. Systematic Random Sample - Answer>> A sample where every kth individual is selected from a list or queue.
Test Statistic - Answer>> The number of standard deviations (standard errors) that a sample statistic lies from a hypothesized population parameter. Third Quartile - Answer>> Symbolized Q3, represents the median of the upper 50% of a data set. Transformation - Answer>> Changing the values of a data set using a mathematical operation. Treatments - Answer>> Combinations of different levels of the factors in an experiment. Two-Way Table - Answer>> A frequency table that displays two categorical variables. Type I Error - Answer>> Rejecting a null hypothesis when it is in fact true. Type II Error - Answer>> Failing to reject a null hypothesis when it is in fact false. Undercoverage - Answer>> When some individuals of a population are not included in the sampling process. Uniform - Answer>> All data values in the distribution have similar frequencies. Unimodal - Answer>> A distribution with a single, clearly defined, peak.
