ANSWER KEYS - Teacher Use Only

Sampling & Inference | Grade 7

Student Concept Worksheet Answers
1
a) RANDOM | b) BIASED - moviegoers prefer movies | c) RANDOM
a) Systematic selection from alphabetical list is random. b) People at a theater already like movies. c) Computer random selection is truly random.
2
a) 40% | b) 180 students
a) 24/60 = 0.40 = 40%. b) 0.40 x 450 = 180 students.
3
C - Randomly select 100 customers
A is biased (only unhappy). B is biased (only happy). D is not customers' opinions. C gives everyone an equal chance.
4
a) 45/75 = 3/5 or 60% | b) 7,200 voters
a) 45/75 simplifies to 3/5 or 60%. b) 0.60 x 12,000 = 7,200 voters.
Practice Worksheet Answers

Part A: Random or Biased

#AnswerExplanation
1BIASEDStudents in lunch line already eat cafeteria food; doesn't include students who bring lunch or skip
2RANDOMComputer random selection gives everyone equal chance
3BIASEDOnly people who care enough to call; voluntary response bias
4BIASEDLibrary visitors read more than average population
5RANDOMDrawing names without looking = equal chance

Part B: Making Predictions

6
a) 60% | b) 360 students
a) 30/50 = 0.60 = 60%. b) 0.60 x 600 = 360 students.
7
a) 4/80 = 1/20 or 5% | b) 250 bulbs
a) 4/80 = 0.05 = 5%. b) 0.05 x 5,000 = 250 defective bulbs.
8
a) 60% | b) 9,000 voters
a) 72/120 = 0.60 = 60%. b) 0.60 x 15,000 = 9,000 voters.
9
a) 70% | b) 5,950 customers
a) 140/200 = 0.70 = 70%. b) 0.70 x 8,500 = 5,950 customers.

Part C: Which Method is Best

10
B - Randomly select 200 customers from database
A captures only negative, C captures only positive, D is not customers. B is unbiased.
11
C - Randomly selected phone numbers across the country
A/D favor sports fans, B might work but limited location. C reaches diverse population.

Part D: Word Problems

12
a) 252 | b) 216 | c) 108
a) 42/150 = 28%, 0.28 x 900 = 252. b) 36/150 = 24%, 0.24 x 900 = 216. c) 18/150 = 12%, 0.12 x 900 = 108.
13
a) Similar | b) 816 students | c) Larger sample = more reliable
a) 70% and 68% are close. b) 0.68 x 1,200 = 816. c) Larger samples have less variability.
14
Challenge - sample answers provided
a) All students at the school. b) Assign numbers, use random generator; draw names from hat; select every nth student. c) 50-100 reasonable. d) Only asking morning people, or just athletes, etc.
FAST Practice Quiz Answers
1
C) Randomly select 50 students from enrollment list
A is biased (only cafeteria users), B is biased (just one club), D is biased (teacher selection). C is random.
2
C) 1,300
52/80 = 0.65 = 65%. 0.65 x 2,000 = 1,300 satisfied customers.
3
B) The sample is biased - gym members are more likely to exercise
Gym members don't represent all Americans. This is location bias. Sample size (A) is okay. More gyms (D) doesn't fix the bias.
4
Select: Random number generator, Every 5th person, Drawing names from hat
Random number generator - random
Volunteers - biased (self-selection)
Every 5th person - systematic random
Names from hat - random
Friends - biased (convenience sample)
5
C) 15,000
75/150 = 0.50 = 50% support A. 0.50 x 30,000 = 15,000 voters.
6
B) Sample B is likely more reliable because it is larger
Larger random samples are more reliable. The percentage being higher (A) doesn't mean better. Both are valid (not D), but not equally reliable (not C).
FAST Quiz Scoring Guide
ScoreInterpretationRecommended Action
6/6MasteryReady for more complex data analysis and statistical inference
4-5/6Approaching MasteryReview specific areas (bias identification or prediction calculations)
2-3/6DevelopingReteach with concrete examples using manipulatives
0-1/6Needs InterventionSmall group instruction focusing on population vs sample concepts first
FAST Success Kit | Grade 7 | FL B.E.S.T. Standards: MA.7.DP.1.1, MA.7.DP.1.2, MA.7.DP.1.3 | Answer Key - Teacher Use Only