Applications of Statistics Practice Questions with complete Solutions 100% Pass

Applications of Statistics Practice Questions with complete Solutions 100% Pass categorical variable - Answers divides the cases into groups, placing each case into exactly one of two or more categories quantitative variable - Answers measures or records a numerical quantity for each case. Numerical operations like adding and averaging make sense for this. explanatory variable - Answers the former, independent variable (x axis) response variable - Answers the latter, dependent variable (y axis) population - Answers includes all individuals or objects of interest sample - Answers subset of a population statistical inference - Answers the process of using data from a sample to gain information about the population sampling bias - Answers occurs when the method of selecting a sample causes the sample to differ from the population in some relevant ay. If this exists we cannot trust generalizations from the sample of the population simple random sample - Answers (n units), all groups of size n in the population have the same chance of becoming the sample. Avoids sampling bias bias - Answers occurs when the method of collecting data causes the sample data to inaccurately reflect the population associated - Answers if values of one variable tend to be related to the values of the other variable causation - Answers if changing the value of one variable influences the value of the other variable confounding variable - Answers third variable that is associated with both the explanatory and response variables. Plausible explanation for the two variables being associated experiment - Answers is a study in which the researcher actively controls one or more of the explanatory variables observational study - Answers is a study in which the researcher does not acitvely control the value of any variable but simple observes the values as they naturally exist randomized experiment - Answers the value of the explanatory variable for each unit is determined randomly, before the response variable is measured randomized comparative experiment - Answers we randomly assign cases to different treatment groups and then compare results on the response variables matched pairs experiment - Answers each case gets both treatments in random order, and we examine individual differences in the response variable between the two treatments proportion - Answers proportion in a category = # in that category / total # proportion sample notation - Answers p (hat) proportion population notation - Answers p two-way variable - Answers used to show the relationship between two categorical variables. The categories for one variable are listed down the side (rows) and the categories for the second variable are listed across the top (columns). outliers - Answers the observed value that is notably distinct from the other values in a dataset. symmetric - Answers if the two sides approximately match when folded on a vertical center line skewed to the right - Answers if the data are piled up on the left and the tail extends relatively far out to the right skewed to the left - Answers if the data are piled up on the right and the tail extends relatively far out to the left bell-shaped - Answers if the data are symmetric and shaped in the form of a bell mean - Answers = X1+X2+...+Xn / n mean of sample notation - Answers x-bar mean of population notation - Answers greek letter "mu" median notation - Answers m median - Answers the middle entry if an ordered list of the data values contains an odd number of entries, or the average of the middle two values if an ordered list contains and even number of entries (splits data in half) resistant - Answers a statistic that is relatively unaffected by extreme values. The median is resistant, while the mean is not standard deviation - Answers measures the spread for a quantitive variable. rough estimate of the typical distance of a data value from the mean. standard deviation sample notation - Answers s standard deviation population notation - Answers sigma The 95% rule - Answers if a distribution of data is approximately symmetric and bell-shaped, about 95% of the data should fall within two standard deviations of the mean. This means that about 95% of the data in a sample from a bell-shaped distribution should fall in the interval from "x-bar"-2s to "x-bar"+2s number of standard deviations from the mean - Answers z-score z-score - Answers z-score = (mean of pop - mean of sample) / stand. dev. tells how many standard deviations the value is from the mean, and is independent of the unit of measurement Pth percentile - Answers the value of a quantitative variable which is greater than P percent of the data Five Number Summary - Answers minimum, Q1, median, Q3, maximum Q1 - Answers = first quartile = 25th percentile Q3 - Answers = third quartile = 75th percentile Range - Answers maximum - minimum Interquartile Range (IQR) - Answers Q3-Q1 detection of outliers - Answers smaller than Q1 - 1.5(IQR) larger than Q3 + 1.5(IQR) box plot - Answers Q1 to Q3 with median in the middle draw lines to the most extreme value that is not an outlier analyzing a single quantitative variable (difference from a matched pairs setting) - Answers dotplot, histogram, boxplot use 95% rule identify outliers by 1.5(IQR) rule five number summary, mean, median, SD, IQR analyzing a single categorical variable (matched pairs) - Answers bar chart, pie chart frequency, relative frequency, proportion analyzing relation between one categorical and one quantitative - Answers side-by-side box plot, dot plot, histogram statistics for the quantitive variable within each category, difference in means