STT 350: Survey sampling Dr. Cuixian Chen Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow STT 350: Survey sampling Dr. Cuixian Chen Review Review section for Final Exam

Ex 4.1, page 102 List all possible simple random samples (SRS) of size n=2 that can be selected from the population {0, 1, 2, 3, 4}. Q: Calculate sigma-square for the population and V(y-bar). That is to find the population variance and sample variance of y-bar. Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 9

Review: 4.6 Comparing two Estimates After estimating individual parameters, such as means, or proportions, we often want to compare the estimates of two parameters. Whether using means or proportions, comparisons are usually made by way of differences.

Review: 4.6 Comparing two Estimates Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 9

4.6 Comparing two Means When comparing means, we consider only the independent- sample case because the dependent case becomes too complicated to handle at this level. With fpc: Without fpc: Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 4

Eg 4.10, page 95 Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 9

Eg 4.10, page 95 Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 9

Eg 4.10, page 95 Use Excel or R to complete the following exercises: (a) Comparing lake types 1 and 2, what is your best estimate of the difference in mean mercury levels for these two types of lakes? (b) Is there sufficient evidence to conclude that the mean mercury level for lakes of type 1 differs from that for lakes of type 2? (c) Is there sufficient evidence to conclude that the mean mercury level for lakes of type 1 differs from that for lakes of type 3? (d) Is there sufficient evidence to conclude that the mean mercury level for lakes of type 2 differs from that for lakes of type 3? Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 9

EX4.18, page 104: comparing means Without fpc: Chapter 4

4.6 Comparing two Proportions When comparing proportions, however, a commonly occurring dependent situation does have a rather simple solution. For independent situation, covariance=0. Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 4

Eg4.11, page 98 Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 4

Extra Examples A question asked to high school students was if they lied to a teacher at least one during the past year. The information is presented below Male Female Lied at least once Yes 3228 10295 No 9659 4620 Find the estimated difference in proportion for those who lied at least once to the teacher during the past year by gender. Place a bound on this estimated difference.* *Source: Moore, McCabe and Craig

Extra Multinomial example If statistics are from a multinomial distribution, then cov(qhat1,qhat2) = (-p1p2/n) In a class with 30 students, the table below illustrates the breakdown of class: Freshmen 10 Sophomore 5 Junior 7 Senior 8 Estimate the difference in percent Freshmen and percent Junior and place a bound on this difference.

4.6 Comparing two Means When comparing means, we consider only the independent- sample case because the dependent case becomes too complicated to handle at this level. With fpc: Without fpc: Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 4

4.6 Summary: Comparing two estimates When comparing proportions, however, a commonly occurring dependent situation does have a rather simple solution. Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow Chapter 4