Note that: The conclusion that the sampling distribution has the same mean as Y does involve either of the model assumptions. not The independence assumption is needed for of the other both two conclusions (that the sampling distribution is normal and that the sampling distribution has standard deviation ). Forming the confidence interval proceeds by the following steps: we specify some high degree of probability; this called the use 0.95 to illustrate; so we’ll say confidence level. (We’ll “95% confidence level.”) The trial two conclusions of the theorem (that the sampling distribution of is normal with mean imply that there is µ) number so that a (*) The probability that lies between - a and + a is 0.95: µ µ P(µ - a < < + a) 0.95 µ [Draw a picture of the sampling distribution to help see why!] It’s important to keep in mind what is a random Caution: variable and what is a constant: Is a constant or a random variable? _______________ µ Is a constant or a random variable? ________________ a Is a constant or a random variable? ________________
Note that: The conclusion that the sampling distribution has the same mean as Y does not involve either of the model assumptions. The independence assumption is needed for both of the other two conclusions (that the sampling distribution is normal and that the sampling distribution has standard deviation ). Forming the confidence interval proceeds by the following steps: we specify some high degree of probability; this called the confidence level. (We’ll use 0.95 to illustrate; so we’ll say “95% confidence level.”) The two conclusions of the theorem (that the sampling distribution of is normal with mean µ) imply that there is number a so that (*) The probability that lies between µ - a and µ + a is 0.95: P(µ - a < < µ + a) 0.95 [Draw a picture of the sampling distribution to help see why!] Caution: It’s important to keep in mind what is a random variable and what is a constant: Is µ a constant or a random variable? _______________ Is a a constant or a random variable? ________________ Is a constant or a random variable? ________________ trial
WorkshopSlidesDayTwo2017-part3.docx