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

Types of Random SamplingSPLIT POPULATION INTO GROUPS?yesnoARE THE GROUPS REPRESENTATIVE?EVERY SUBSET HAS EQUAL CHANCE?yesnoyesnoStratified SampleCluster SampleSimple Random SampleSystematic Sample

Types of Random SamplingSPLIT POPULATION INTO GROUPS?yesnoARE THE GROUPS REPRESENTATIVE?EVERY SUBSET HAS EQUAL CHANCE?yesnoyesnoStratified SampleCluster SampleSimple Random SampleSystematic SampleExample 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.

Types of Random SamplingSPLIT POPULATION INTO GROUPS?yesnoARE THE GROUPS REPRESENTATIVE?EVERY SUBSET HAS EQUAL CHANCE?yesnoyesnoStratified SampleCluster SampleSimple Random SampleSystematic SampleExample 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

Types of Random SamplingSPLIT POPULATION INTO GROUPS?yesnoARE THE GROUPS REPRESENTATIVE?EVERY SUBSET HAS EQUAL CHANCE?yesnoyesnoStratified SampleCluster SampleSimple Random SampleSystematic SampleExample 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.

Types of Random SamplingSPLIT POPULATION INTO GROUPS?yesnoARE THE GROUPS REPRESENTATIVE?EVERY SUBSET HAS EQUAL CHANCE?yesnoyesnoStratified SampleCluster SampleSimple Random SampleSystematic SampleExample 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

Understanding Cross Tabs

Left HandedRight HandedFemale36328Male35240

Understanding Cross Tabs

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Left Handed:71/639 = 11.1%

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female:364/639 = 57.0%

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female and Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female and Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female and Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female and Left Handed:36/639 = 5.6%

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female and Left Handed:36/639 = 5.6%intersection

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed and Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed and Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed and Left Handed:0/639 = 0.0%

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

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

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Female or Left Handed:(36+328+35)/639 = 62.4%all numbers

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed or Left Handed:

Left HandedRight HandedFemale36328364Male3524027571568639

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

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed:females

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed:females

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed:females

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are Right Handed:females328/364 = 90.1%

Left HandedRight HandedFemale36328364Male3524027571568639

Understanding Cross TabsPercentage of students that are not Right Handed:71/639 = 11.1%

Left HandedRight HandedFemale36328364Male3524027571568639

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

Left HandedRight HandedFemale36328364Male3524027571568639