7th Grade Random Sampling and Inference Worksheet Solutions (PDF)
This random sampling answers for 7th Grade covers random sampling and inference (Common Core 7.SP.A.1, 7.SP.A.2), with a free PDF to print.
Use this answer key to check your work on the random sampling worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.
Grade 7 · Common Core State Standards: 7.SP.A.1, 7.SP.A.2
Random sampling answers: exercises 1 to 10
Exercise 1 – Population and sample
Population: all 600 students.
Sample: the 40 students surveyed.
Population: 600 students; sample: 40 students
Exercise 2 – Biased or not?
No. Team members are more likely to like basketball than other students, so the sample is biased.
Biased
Exercise 3 – Random method
(b) gives every student an equal chance of being chosen.
(a) favors students who arrive early.
(b)
Exercise 4 – Pizza estimate
Sample proportion: \(50\div 200=0.25=25\%\).
\(0.25\times 1200=300\)
About 300 students
Exercise 5 – Library visits
\(18\div 60=0.3\).
\(0.3\times 800=240\)
About 240 students
Exercise 6 – Marbles in a jar
\(7\div 25=0.28\).
\(0.28\times 400=112\)
About 112 red marbles
Exercise 7 – Sample size
Larger random samples vary less, so Jamal’s estimate is likely to be closer.
Jamal’s sample of 100
Exercise 8 – Election poll
\(96\div 150=0.64=64\%\).
\(0.64\times 12500=8000\)
About 8,000 voters
Exercise 9 – Quality control
\(8\div 200=0.04\).
\(0.04\times 5000=200\)
About 200 chargers
Exercise 10 – Tag and count
In the sample, \(\frac{5}{40}=\frac{1}{8}\) of the fish are tagged.
So the 50 tagged fish are about \(\frac{1}{8}\) of all fish: \(50\times 8=400\)
About 400 fish
Exercises 11 and up
Exercise 11 – Question wording
The wording suggests the answer the writer wants, so more people will say yes.
The question leads respondents
Exercise 12 – Random numbers
Skip the repeated number 7.
7, 22, 15, 30, 3
Exercise 13 – Mean of samples
\((22+25+19+24)\div 4=90\div 4=22.5\)
22.5 minutes
Exercise 14 – Compare two samples
Order: 4, 5, 5, 6, 6, 6, 7, 7, 8. The median is the fifth value, 6.
\(6\div 20=0.30=30\%\)
Median 6; about 30%
Exercise 15 – Cafeteria
\(36\div 120=0.3\).
\(0.3\times 900=270\)
About 270 students
Exercise 16 – Bike riders
\(12\div 50=0.24\).
\(0.24\times 2500=600\)
About 600; a sample can differ from the whole population
Exercise 17 – Two samples
Chance causes sampling variability: random samples differ.
Combine the samples or use a larger sample: \(\frac{6+4}{20}=50\%\).
Both vary by chance; use a larger sample
Exercise 18 – Movie night
\(45\div 150=0.3\).
\(0.3\times 3000=900\) want comedy; \(3000-900=2100\) do not.
About 900 want comedy; about 2,100 do not
Exercise 19 – Park survey
\(9\div 30=0.3\).
\(0.3\times 10000=3000\).
A small sample varies a lot; a larger sample would give a more reliable estimate.
About 3,000
Exercise 20 – Hours of sleep
Sum: \(7+7+7+8+8+8+8+8+9+9+9+10=98\).
\(98\div 12\approx 8.2\)
About 8.2 hours
Key facts behind this random sampling answers
- A population is the whole group; a sample is a part of it.
- A random sample gives every member an equal chance of being chosen.
- Biased samples over-represent some members and give poor estimates.
- Estimate a population count by multiplying the sample proportion by the population size.
- Larger random samples vary less and give better estimates.
How to use this random sampling answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
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