STAT EXAM 2 review solution, Exams of Statistics

STAT EXAM 2 review solution update

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2024/2025

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STAT EXAM 2 review solution
descriptive statistics - numerical and graphical summaries are used to characterize a data set or
describe a relationship between two variables (range mean)
inferential statistics - sample date is used to make conclusions about a broader range of individuals
than just those who were observed
fundamental rule for using data for inference - data can be used to make an inference about a much
larger group if the sample can be considered to be representative of the population in respect to the
question of interest
population - the entire group of units about which inferences will be made
sample - the group of units that are actually measured or surveyed
simple random sample - the list of units from which the sample is selected. every unit of the
population has the same chance of being selected
sampling frame - the list of units from which the sample is selected. problem occurs when its not the
same as the target population
census - when every unit of the population is measured or surveyed
bias - a survey is considered if the method used to get the value for the dataset consistently produces
values that are too high or too low
selection bias - when the method used for selecting participants for the survey does not produce a
sample that reflects the population being studied
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STAT EXAM 2 review solution descriptive statistics - numerical and graphical summaries are used to characterize a data set or describe a relationship between two variables (range mean) inferential statistics - sample date is used to make conclusions about a broader range of individuals than just those who were observed fundamental rule for using data for inference - data can be used to make an inference about a much larger group if the sample can be considered to be representative of the population in respect to the question of interest population - the entire group of units about which inferences will be made sample - the group of units that are actually measured or surveyed simple random sample - the list of units from which the sample is selected. every unit of the population has the same chance of being selected sampling frame - the list of units from which the sample is selected. problem occurs when its not the same as the target population census - when every unit of the population is measured or surveyed bias - a survey is considered if the method used to get the value for the dataset consistently produces values that are too high or too low selection bias - when the method used for selecting participants for the survey does not produce a sample that reflects the population being studied

non participation bias - when a representative sample is chose however some of the individuals selected for the survey do not participate either because they could not be contacted or they just didnt respond. can lead to systematically overestimating/ underestimating the truth about a population biased response - when someone in the study provides incorrect information margin of error - a measure of the accuracy of a sample proportion as an estimate of the population portion conservative margin of error - 1/squareroot of n confidence interval - an interval of values that estimates an unknown population parameter choice of sample size - often the sample size is determined by the desired margin of error for a 95% confidence interval solving for n - n=1/(margin of error in decimal form)^ stratified random sample - the population is divided into groups and then a simple random sample is taken from each group strata - term for subgroups of a population clustering sampling - the population is divided into groups. one or more groups are randomly selected and then all individuals in the selected groups are surveyed systematic sampling - the list of participants is divided into many consecutive segments. starting point is randomly chosen and then you sample at that same point in each section

subjects - this means that the same thing as experimental units however subjects are used when experimental people are units participants - subjects explanatory variable - independent variable response variable - dependent variable confounding variables - a variable that affects the response variable and its related to the explanatory variable lurking variable - a potentially confounding variable that is not taken into account in the interpretation of the study two independent samples - each experiment unit receives one treatment, is in one group, and provides one measurement two dependent samples - does all things and receives all treatments, provides all measurements experiment - when the effect of manipulating the environment of participants is measured in some way volunteers - the participants in a randomized experiment randomization - the random assignment of treatments or conditions

randomizing the type of treatment - protects against unknown biases and confounding variables and it prevents the researchers from making assignments that are favorable to their hypothesis carry over effect - what happens when the first measurement affects what happens with the second replication in statistics - assigning more than one experimental unit to each treatment condition replication in science - a more general use of the term. that means that independent researchers should be able to reproduce findings double dummy experiments - each group is given one placebo and one active treatment randomized block design - an experiment where participants are first divided into homogenous blocks and then treatments are randomly assigned to one or more participants within matched pair design - a special case where participants are first matched based on an important characteristic then each member matched is given a different treatment repeated measures design - each participant receives all treatments ideally in a different order retrospective study - participants are asked to recall past events prospective study - researchers follow participants into the future so they can record the events as they happen case control study - participants are compared to a control group

mutually exclusive events - two events that cant happen at the same time disjointed - = mutually exclusive independent events - knowing that one event will occur does not change the probability that the other occurs dependent events - knowing that one event occurs changes the probability that the other occurs conditional probability - event b given that event a already happened is the long run relative frequency with which event b occurs when circumstances are such that a has occurred P(B) - notation for the unconditional probability that event b occurs P(B|A) - notation for the conditional probability that event B occurs given that A already happened complement rule - the probability of an event plus the probability of the complement to that event equals 1 equation for the complement rule - p(a)+p(ac)= independence rule - if two events are independent the probability of their intersection is equal to the product of the individual probabilities equation for the independence rule - p(a and b) = p(a) x p(b)

addition rule for union - the probability of the union of two events is found by adding the individual event probabilities than subtracting the joint addition rule for union equation - p(a or b) = p(a) + p(b) - p( a and b) conditional probability - the numerator is the probability of the intersection of the two events and the denominator is the probability of the given event conditional probability equation - p(a|b) = p(a and b)/p(b) if two events are mutually exclusive - p(a or b) = P(a) + P(b) - 0 if two events are independent - p(a|b) = p(a) specificity - proportion of the people who are correctly negative and falsely positive (1-false positive) sensitivity - proportion of people who correctly test positive and falsely negative gamblers fallacy - a misconception where people think the long run probability of an even should apply in the short run. primarily applies to independent events law of small numbers - people make conclusions on the entire population but the sample sizes are too small