Midterm 1 Review

1. Midterm 1 Review (1) Types of Random Samples (2) Percentages & Crosstabs

2. Types of Random Sampling SPLIT POPULATION INTO GROUPS? no yes ARE THE GROUPS REPRESENTATIVE? EVERY SUBSET HAS EQUAL CHANCE? no no yes yes Stratified Sample Cluster Sample Systematic Sample Simple Random Sample

3. Types of Random Sampling SPLIT POPULATION INTO GROUPS? no yes ARE THE GROUPS REPRESENTATIVE? EVERY SUBSET HAS EQUAL CHANCE? no no yes yes Stratified Sample Cluster Sample Systematic Sample Simple Random Sample Example 1: We want to know what proportion of Akron Statistics students are right handed. Currently, there are 20 Statistics classes throughout the week. We randomly choose three of these classes and take for our sample all students in these three classes. Cluster Sample: Each class is a representative group of the population. The proportion of right handed students should be close to the same for all classes.

4. Types of Random Sampling SPLIT POPULATION INTO GROUPS? no yes ARE THE GROUPS REPRESENTATIVE? EVERY SUBSET HAS EQUAL CHANCE? no no yes yes Stratified Sample Systematic Sample Cluster Sample Simple Random Sample Example 2: We want to know about the age of Akron Statistics students. We decide to randomly assign numbers to students using Minitab and choose the students with the lowest 100 numbers to survey. Simple Random Sample (SRS): Any subset of the population of 100 students has an equal chance of being selected

5. Types of Random Sampling SPLIT POPULATION INTO GROUPS? no yes ARE THE GROUPS REPRESENTATIVE? EVERY SUBSET HAS EQUAL CHANCE? no no yes yes Stratified Sample Cluster Sample Systematic Sample Simple Random Sample Example 3: We want to know about the age of Akron Statistics students. Historically, night students are older on average than day students. We randomly choose 5 students from classes that begin after 5pm and 20 students from classes that begin before 5pm. Stratified Sample: Each group is a non-representative group of the population. If instead we chose a sample of 25 night time students, we would have a biased sample. This could happen “accidently” with SRS.

6. Types of Random Sampling SPLIT POPULATION INTO GROUPS? no yes ARE THE GROUPS REPRESENTATIVE? EVERY SUBSET HAS EQUAL CHANCE? no no yes yes Stratified Sample Cluster Sample Systematic Sample Simple Random Sample Example 4: We want to know about the age of the 600 Akron Statistics students. Flip a coin. If heads then start with the first name on an alphabetical list containing all Akron Stats students, and select for your sample every other student. If tails, then start with the second name on the list, and select for your sample every other student. (sample size = 300) Systematic: Although each individual has a 50% chance of being selected, there is a group (namely the two students at the beginning of the list) that have no chance of being selected together

7. Understanding Cross Tabs

8. Understanding Cross Tabs

9. Understanding Cross Tabs Percentage of students that are Left Handed: 71/639 = 11.1%

10. Understanding Cross Tabs Percentage of students that are Female: 364/639 = 57.0%

11. Understanding Cross Tabs Percentage of students that are Female and Left Handed:

12. Understanding Cross Tabs Percentage of students that are Female and Left Handed:

13. Understanding Cross Tabs Percentage of students that are Female and Left Handed:

14. Understanding Cross Tabs Percentage of students that are Female and Left Handed: 36/639 = 5.6%

15. Understanding Cross Tabs Percentage of students that are Female and Left Handed: 36/639 = 5.6% “intersection”

16. Understanding Cross Tabs Percentage of students that are Right Handed and Left Handed:

17. Understanding Cross Tabs Percentage of students that are Right Handed and Left Handed:

18. Understanding Cross Tabs Percentage of students that are Right Handed and Left Handed: 0/639 = 0.0%

19. Understanding Cross Tabs Percentage of students that are Female or Left Handed:

20. Understanding Cross Tabs Percentage of students that are Female or Left Handed:

21. Understanding Cross Tabs Percentage of students that are Female or Left Handed:

22. Understanding Cross Tabs Percentage of students that are Female or Left Handed:

23. Understanding Cross Tabs Percentage of students that are Female or Left Handed: (36+328+35)/639 = 62.4%

24. Understanding Cross Tabs Percentage of students that are Female or Left Handed: (36+328+35)/639 = 62.4% “all numbers”

25. Understanding Cross Tabs Percentage of students that are Right Handed or Left Handed:

26. Understanding Cross Tabs Percentage of students that are Right Handed or Left Handed:

27. Understanding Cross Tabs Percentage of students that are Right Handed or Left Handed:

28. Understanding Cross Tabs Percentage of students that are Right Handed or Left Handed: (36+328+35+240)/639 = 100.0%

29. Understanding Cross Tabs females Percentage of students that are Right Handed:

30. Understanding Cross Tabs females Percentage of students that are Right Handed:

31. Understanding Cross Tabs females Percentage of students that are Right Handed:

32. Understanding Cross Tabs females Percentage of students that are Right Handed: 328/364 = 90.1%

33. Understanding Cross Tabs Percentage of students that are not Right Handed: 71/639 = 11.1%

34. Understanding Cross Tabs Short-hand Notation: Let F=Female, M=Male R=Right Handed, L=Left Handed Percentage of students that are Left Handed: P[L]= 71/639 Percentage of students that are Female: P[F]= 364/639 Percentage of students that are Left Handed and Female: P[L and F] = 36/639 Percentage of students that are Left Handed or Female: P[L or F] = (36+328+35)/639 Percentage of females that are Right Handed: P[R | F] = 328/364 Percentage of students that are not Right Handed: P[not R] = 71/639