STAT 210 1nd EditionExam # 7 Study Guide Lectures: 37-41Lecture 37 (November 19)- Sampling Distribution of ´X1−´X2- Statistical inferences involve the use of statistics calculated from sample data to make statements about population parameters that are unknown. o Includes confidence intervals & significance tests- This chapter deals with making statistical inferences about the difference between two population means µ1 - µ2- Identify populations & parameters then samples selected from the populations. o Simple random sample of n1 from 1st population and simple random sample of n2 from second. Then compute the sample means ´X1∧´X2o The point estimate µ1 - µ2 is the difference in sample meanso Samples can be selected independently or dependently of each other. - Assume the 2 samples are independent of one another in this chapter. Possibility that n1 and n2 won’t be same. - Sampling distribution assumptionso Have 2 independent simple random sampleso Either both populations normally distributed or both sample sizes are large enough for CLT to apply- Know the formula for the sampling distribution for the difference in sample means- Know z-score transformation formula- Keep in mind, formulas given for exams. Be able to recognize which formula to use when. - Go through examples from lecture and practice problems. Lecture 38 (November 21)- Confidence Intervals for µ1 - µ2- Know sampling distribution assumptions (same as for lecture 37)- Because population means unknown, must be estimated- Confidence Interval for µ1 - µ2 Assumptionso Have 2 independent simple random sampleso Either both populations normally distributed or populations large enough for CLT to applyo Population standard deviations σ1 and σ2 are known - If assumptions satisfied, 100*C% confidence interval for µ1 - µ2 can be determined using the formula & t-table - When σ1 and σ2 are unknown must use t statistic o Degrees of freedom equal to the smaller of n1-1 and n2-1- Go through examples from lecture and practice problems.Lecture 39 (November 24)- Statistical Tests of µ1 - µ2- Tests of Significance for µ1 - µ2o H0: µ1 - µ2 = 0o Ha: µ1 - µ2 > 0o Ha: µ1 - µ2 < 0o Ha: µ1 - µ2 ≠ 0- When standard deviations known use standard normal (Z) distribution, when unknown use t distribution - Decision & conclusion determined the same as for all other tests- Go through examples from lecture and practice problems. Lecture 40 (November 26)- Statistical Tests of µ1 - µ2 Paired Data- Suppose two samples are dependent or paired- Tests of significance same- Select srs of n subjects, make 2 measurements on each subject, for each subject in sample can compute difference between 2 measurements d = X1 – X2, this generates a sample of n differences d1, d2, … dn. - Assumptionso SRS selected with 2 measurements on each subjecto Differences are normally distributed or sample size is large enough for CLT to apply- Paired t-test is a regular t-test with ´Xd being the mean of the n differences and sd beingthe standard deviation of the n differences. - Go through examples from lecture and practice problems. Lecture 41 (December 1)- Inferences for Comparing 2 Population Means- This lecture just a wrap up of the previous lectures- Go through examples from lecture and practice