STATS 250 1st Edition Lecture 4 Outline of Last Lecture I. Collecting and Using Sample Data WiselyII. Margin of Error, Confidence Intervals, and Sample SizeIII. How to Ask Survey QuestionsOutline of Current Lecture I. Types of Research Studies and VariablesII. Interpretations of ProbabilityIII. Basic Rules of Finding ProbabilityCurrent LectureI. Types of Research Studies and Variablesa. Observational Studies: researchers simply observe or measure the participants and do not assign any treatments or conditions. Participants are not asked to do anything differentlyb. Experiments: researchers manipulate something and measure the effect of the manipulation on some outcomes of interest. Often participants are randomly assigned to the various conditions or treatmentsc. Explanatory variable: variable that affects response/outcome variabled. Response/Outcome variable: variable affected by explanatory variablee. Confounding variable: variable that both affects the response variable and also is related to the explanatory variable. Effect on response and explanatory variables cannot be separatedi. If left unmeasured, they are called lurking variablesii. Most problematic in observational studiesThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.II. Interpretations of Probabilitya. Personal/Subjective Probability: P(A) = the degree to which a given individual believes that the event A will happenb. Long Term Relative Frequency: P(A) = proportion of times A occurs if the random experiment is repeated over and overc. Basket Model: P(A) = proportion of balls in the basket that have an A on themIII. Basic Rules of Finding Probabilitya. Always has a value between 0 and 1b. Complement rule: P(AC) = 1 – (A)i. Probability that not A occurred c. Addition rule: P(A or B) = P(A) + P(B) – P(A and B)i. Probability that A or B occurredd. Multiplication rule: P(A and B) = P(A)*P(B)i. Probability that A and B occurrede. Conditional probability: P(A|B) = P(A and B)/P(B)i. Probability that A will happen if B happensf. Mutually Exclusive: two events do not contain any of the same outcomesg. Independent: if one event occurs it does not change the probability that the other occursi. P(A|B)=