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Correct Answers 2024-2025. Graded A
"And" Probability for Dependent Events - ANSThe probability that two events both occur is the probability of the first event times the conditional probability that the second event occurs, given that the first already has. Also known as the "General Multiplication Rule". "And" Probability for Independent Events - ANSA way to approximate probability based on trials of chance experiments that mimic the real-life trials. Also known as the "Special Multiplication Rule". "Or" Probability - ANSThe probability that at least one of two events, A or B, occur. 1.5xIQR rule - ANSStep 1: Find the quartiles of the data set. Step 2: Find the interquartile range (IQR). Step 3: If we have a point that is 1.5 IQR's below the first quartile or 1.5 IQR's or more above the third quartile, then it is an outlier.
If a point is larger than Q3 + 1.5xIQR, or smaller than Q1 - 1.5xIQR, then it is an outlier. 68-95-99.7 rule - ANSA rule that applies to normal distributions, stating that 68% of all data points fall within one standard deviation of the mean, 95% of all data points fall within two standard deviations of the mean, and 99.7% of all data points fall within three standard deviations of the mean. Absolute Change - ANSThe raw increase or decrease in the value of a variable Accuracy - ANSThe extent to which the values, when considered all together, center around the correct value for a variable. alternative hypothesis - ANSA claim that a population parameter differs from the value claimed in the null hypothesis. Analysis of Variance (ANOVA) - ANSA hypothesis test that allows us to compare three or more population means. available data - ANSData collected by some other entity - a government organization or private company.
The tendency for collected data to differ from what is expected in a systematic way. Biased data can often favor a specific group of those studied. big idea - ANSEach distribution has its own situation for which it is ideal. The data will determine which distribution is best to use. big idea - ANSNote, the main overarching point here is to divide each cumulative by the total. big idea - ANSOutliers are important data points because they are so high or low that they would be considered unusual. big idea - ANSThe binning process is important. Problems can arise if you make the bins too narrow. In the previous examples, there were bins of width 10 degrees and bins of width 5 degrees. You could have decided on bins with width 1 or 2 degrees, but perhaps you wouldn't have gotten the same overall shape of the distribution. big idea - ANSThe sample should represent the group/population at large, so it's important individuals are selected carefully for the sample. That way, accurate
information will be gained and can be used to describe the group/population at large. big idea - ANSThere are certain instances in which an observational study will be preferred over an experiment due to factors like time, money, and privacy, where it is unlikely people will divulge that type of information big idea - ANSUni means one, bi means two, and modal means the number of modes each distribution has. big idea - ANSYou can't make useful statistics out of poor data. Thinking critically will help you determine which type of data should be used for your purposes. Bimodal Distribution - ANSA distribution where there are two distinct values or bins that contain more data than the others, usually separated by a gap. binning - ANSThe method of deciding what widths of categories should be used on a histogram.
Step 3: Use the sigma notation, which is the same as summation notation, to add these values. Step 4: Divide that sum by (n minus 1).Step 5: Take the square root. causality - ANSA cause-and-effect relationship between two variables. Causation/Cause-and-Effect - ANSA phenomenon whereby an increase in one variable directly leads to an increase or decrease in another variable. census - ANSUsing the entire population to obtain data. center - ANSThe "middle" of the data set. There are many measures of center. central limit theorem - ANSA theorem that explains the shape of a sampling distribution of sample means. It states that if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal. Central Limit Theorem - ANSA theorem that explains the shape of a sampling distribution of sample means. It states that if the sample size is large (generally n ≥
30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal. chi-square statistic - ANSTake the observed values. Subtract the expected values. Square that difference. Divide by the expected values. Add up all of those fractions. The sum of the ratios of the squared differences between the expected and observed counts to the expected counts. chi-square test for association - ANSStep 1: State the null and alternative hypotheses. Step 2: Check the conditions. Step 3: Calculate the test-statistic and p-value Step 4: Compare your test statistic to your chosen critical value, or your p-value to your chosen significance level. Based on how they compare, state a decision about the null hypothesis and conclusion in the context of the problem.
cluster sample - ANSA sampling method where the population is separated into groups, typically geographically, and a random selection of clusters is made. Each individual in the cluster becomes part of the sample. clusters - ANSSmaller subgroups of the population, not necessarily similar in any way besides all being together in one place, making the individuals easier to sample together. Coefficient of Determination (r^2) - ANSA value that explains the percent of variation in the response variable that can be explained by a linear association with the explanatory variable. It is the square of the correlation coefficient. Complement of an Event}} - ANSSo the probability of green complement is equal to 1 minus the probability of green, or 1 minus 2/38, which equals 36/38. All outcomes not in the given event. Completely Randomized Design - ANSAn experimental design where the assignment of subjects to treatments is done entirely at random
Conditional Probability - ANSThe probability that one event occurs, given that another event has already occurred. Confidence Interval - ANSA range of potential values that the true value could be. It is obtained by adding and subtracting the margin of error from the value in the sample. confidence interval - ANSAn interval that contains likely values for a parameter. We base our confidence interval on our point estimate, and the width of the interval is affected by confidence level and sample size. confidence interval - ANSAn interval we are some percent certain (eg 90%, 95%, or 99%) will contain the population parameter, given the value of our sample statistic. Confidence Interval for a Population Proportion - ANSA confidence interval that gives a likely range for the value of a population proportion. It is the sample proportion, plus and minus the margin of error from the normal distribution. confounding - ANSOccurs when the effects of the treatments, if any, are indistinguishable from the potential effects of some other variable which was unaccounted for.
correlation - ANSA statistic which measures the strength and direction of the linear association between two quantitative variables. correlation - ANSThe strength and direction of a linear association between two quantitative variables. correlation coefficient - ANSThe numerical value between -1 and +1 that measures the correlation between two quantitative variables. critical value - ANSA value that can be compared to the test statistic to decide the outcome of a hypothesis test critical value - ANSA value that can be compared to the test statistic to decide the outcome of a hypothesis test cumulative frequency - ANSThe number of data points that fall within or below a given bin of data. data - ANSInformation used in a study to answer a statistical question.
Data Analysis - ANSThe understanding of the key features of a set of data--shape, center, spread, and outliers. deliberate bias - ANSThe purposeful misrepresentation of data for the purpose of advancing an agenda. dependent events - ANSTwo events where knowing whether the first event occurred affects the probability of the second event occurring. descriptive statistics - ANSWhen you use descriptive statistics, you are going to analyze what's going on at a particular point and use statistics to describe the information that you've obtained. direction - ANSThe way one variable responds to an increase in the other. With a negative association, an increase in one variable is associated with a decrease in the other, whereas with a positive association, an increase in one variable is associated with an increase in the other. Discrete data - ANSData that can only take so many different values.
A distribution where each data point consists of a mean of a collected sample. For a given sample size, every possible sample mean will be plotted in the distribution. Distribution of Sample Proportions - ANSThe distribution of all possible sample proportions for a certain size, n. dot plot - ANSA distribution in which each data value is represented by a dot above that value on an axis. double-blind experiment - ANSAn experiment where neither the subjects nor anyone in contact with them has any knowledge of which subjects are receiving which treatment. Either/Or Probability for Non-Overlapping Events - ANSThe probability that either of two non-overlapping events occurs is the sum of their individual probabilities. Also known as the "Special Addition Rule". adding both
Either/Or Probability for Overlapping Events - ANSThe probability that either of two events occurs is equal to the sum of the probabilities of the two events, minus the joint probability of the two events happening together. Also known as the "General Addition Rule".
Estimate - ANSThe mean value obtained from the sample. If the sample was well- collected, the estimate should be reasonably close to the true value. event - ANSAn outcome or set of outcomes. expected frequencies - ANSThe number of occurrences we would have expected within each of the categories in a qualitative distribution if the null hypothesis were true. Expected Value - ANSThe long-term average value taken by the outcomes from a chance experiment. It does not need to be one of the possible outcomes. experiment - ANSA type of study where researchers impose treatments on the participants or experimental units.
extrapolation - ANSUsing the regression line to make predictions outside the window for which the model was intended. F statistic - ANSThe test statistic in an ANOVA test. It is the ratio of the variability between the samples to the variability within each sample. If the null hypothesis is true, the F statistic will probably be small. false negative - ANSA test states that some condition is absent when, in fact, the condition is present. false positive - ANSA test states that some condition is present when, in fact, the condition is absent. finding r from r squared - ANSStep 1: Take the square root of r2. If only r-squared is given, what you have to do is take the square root to obtain the correlation coefficient, r. Step 2: Look at the graph to determine sign. You also have to look at the graph to find the association--either positive or negative--to determine the sign of the correlation coefficient. first / lower quartile - ANSThe number at which approximately 25% of the data set falls at or below that value.
five number summary - ANSA brief overview of a data set consisting of the minimum, the first quartile, the median, the third quartile, and the maximum. form - ANSThe overall shape of the data points. The form may be linear or nonlinear, or there may not be any form at all to the points if they form a "cloud." frequency - ANSHow often a data value, or range of values, occurs. frequency polygon - ANSA distribution of data that shows both a histogram and its line chart on the same set of axes. frequency table - ANSA table showing the values of the data, and their respective frequencies. fundamental counting principle - ANSIf chance experiment A has m possible outcomes for one trial, and chance experiment B has n possible outcomes for its trial (independent of the first trial), then there are m times n (m x n) potential outcomes when A and B are done together.
