Stat 200 Final Exam Review 2021

1. Explain, recognize, and cite examples of categorical, ordinal, discrete, and continuous variables.  Categorical: raw data made up of group or category names that don’t necessarily have a logical order (Example: eye color, sex, dominant hand)  Ordinal: variable used to describe data when a categorical variable can be put into some natural order (Example: rating opinions from “extremely dissatisfied” …” neutral”… to “extremely satisfied”)  Discrete: has a countable list of distinct possibilities for its value, only fixed amounts; no decimals. (Example: the number of people with green eyes in a sample of 20 people)  Binomial: number of times a result occurs/does not occur in a specific number of independent observations in a random circumstance  Data: Categorical  N is fixed  X = number of successes/failures  All trials are independent; won’t be affected by each other  Example: the number of times a coin lands on head when flipped 10 times  Continuous: can take on any numerical value in range; including decimals (Example: Height - it could be 72.5”)  The probability that a continuous variable is = to a value is 0%  P(X = k) = 0 2. Interpret numerical summaries of center/location (including five-number summaries) and spread; predict how particular changes in data will influence these summaries. 1. Location: What is the center or average of the data?  Mean numerical average of the data. Represented by X-bar (sample mean)  Median the middle value. Half of the data above it, other half  below it. Represented by M (sample median) 2. Spread: what is the spread/variability of the data?  Range = maximum value – minimum value  IQR = Q3 – Q1  Standard Deviation: also called variability. Average distance a value is from the mean. Represented as s (sample standard deviation)  Sensitive measure 3. Shape: what is the shape of the data? (skewed or bell-shaped)  Skewed RIGHT median mean   Skewed LEFT mean median   Symmetric mean = median  4. 5-number summary: This study source was downloaded by from CourseH on 11-16-2021 23:09:14 GMT -06:00 Resistant won’t be changed by outliers (median, IQR) Sensitive will be affected by outliers (mean, standard deviation, range) 3. Use the empirical rule and the standard normal distribution table or calculator to convert among percentages, ranges of scores, and ranges of z-scores for distributions known to be normal.  The Empirical Rule: true for bell-shaped curves  Standardized z-scores: how many standard deviations a value is from the mean o z= observed value−mean standard deviation 4. Identify and interpret slope, intercept, and R-squared values from simple linear regression output; calculate predicted values and residuals. Interpret T-statistic and p-value for the test of the slope coefficient in a regression.  Regression analysis: examines the relationship between a quantitative response variable and one or more quantitative explanatory variables  Regression Line: line that describes the linear relationship between two quantitative variables  y=bo+b1 x  y = y-hat, predicted y or estimated y  bo = y – intercept, point when line crosses the y-axis  b1 = slope of the straight line  x-axis EXPLANATORY variables   y-axis RESPONSE variables  Comparing r to r 2 r r 2 Interpretation Shows direction and strength of relationship Shows amount of variation in y explained by x