STAT 210 1nd EditionExam # 6 Study Guide Lectures: 31-35Lecture 31 (November 5)- Population mean µ- Assume that data for the whole population is unknown, therefore µ is unknown, as such statistical inferences in the form of confidence intervals and statistical tests must be completed. - Make statistical inferences, must first identify population of interest & specific parameter of interest. - From sample data compute sample mean ´Xo Sample mean becomes basis for inferences made about unknown µ- Sampling distributions must describe the shape, center, spread, & unusual features of the distribution. - Assumptionso Data must be a simple random sample from the populationo Population distribution must be normal/large enough for the central limit theorem to apply- If sample size is large enough then distribution of sample proportion ^p is approximately normalo Sample will be large enough if both expected number of successes n and expected number of failures n(1-) are greater than or equal to 10- If sample is less than 15, not large enough. If at least 15, then CLT will apply unless distribution is heavily skewed due to outliers. - Distribution heavily skewed due to outliers, then CLT only applies if sample is at least 40 (40 or more)- If population mean & standard deviation known & both assumptions satisfied, then the sampling distribution of sample mean can be described as:o Center: the mean of ´X is µ´X = µo Spread: the standard deviation of ´Xis σX = σ/√no Shape: the shape will be normalo Unusual features: there will be no unusual features- Make sure to go through examples in textbook and lecture. Lecture 32 (November 7)- Confidence interval- Will NEVER know for sure whether interval contains µo Only way to have 100% confidence is to actually know value of µ- Assumptionso Simple random sample from populationo Either population is normal or sample size large enough for CLT to applyo Standard deviation σ known- Z-Score transformation- Know how to form correct interpretation of confidence interval - Want high confidence and narrow/precise interval- Want margin of error to be as small as possible- Make sure to go through lecture and textbook examples.Lecture 33 (November 10)- When σ is unknown use t-distribution - Z-distribution and t-distribution differ only in standard deviation- Make sure to go through examples in textbook and lecture.Lecture 34 (November 12)- Review general significance testing procedure- Review significance testing for µ- Make sure to go through lecture examples and textbook examplesLecture 35 (November 14)- Same as for lecture