Sampling Techniques Worksheet 1kly8ij - Worksheet: Statistics Name ... - Free Printable

Here is the solution to each multiple-choice question on the statistics worksheet, with a clear explanation for each answer:

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1. What is the best sampling technique to use for determining the average speed of the cars on a section of highway?

✔ Correct Answer: d. a) or b)

Explanation:
Both *simple random sample* and *systematic sample* can be appropriate for this scenario, depending on how you implement them.

- A simple random sample would involve randomly selecting cars (e.g., using license plate numbers or timing random intervals) — but in practice, it’s hard to identify and “select” individual cars randomly on a highway.
- A systematic sample (e.g., measuring every 5th car that passes, or measuring speed at fixed time intervals like every 30 seconds) is often more practical and still provides a representative sample if traffic flow is steady.

Since both methods can produce unbiased estimates when properly implemented, and systematic sampling is often used in such observational settings, d. a) or b) is the best choice.

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2. Which method is most likely to produce a random sample of the members of your class?

✔ Correct Answer: c. writing the name of each student on a separate piece of paper and then drawing these slips from a hat

Explanation:
This is a classic example of simple random sampling — every student has an equal chance of being selected, and selection is done without bias.

- Option a (listing first six who come to mind) → biased by memory/availability.
- Option b (choosing five oldest) → biased by age.
- Option d (first six to arrive) → biased by punctuality.

Only option c ensures randomness and equal probability for all students.

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3. A large corporation wants to find out which benefits plan its employees would prefer. Which procedure would be most likely to obtain a statistically unbiased sample?

✔ Correct Answer: a. surveying a random sample of employees from a list of all employees

Explanation:
To get an unbiased sample, you need to ensure every employee has a known, non-zero chance of being selected — this is achieved by taking a random sample from the complete list of all employees.

- Option b (inviting all via email) → self-selection bias (only those interested respond).
- Option c (suggestion boxes in random locations) → only captures people who happen to see/use them; not random.
- Option d (one member per department) → may be representative of departments, but not necessarily of the whole population unless departments are proportional and individuals within are randomly chosen.

Only a guarantees a statistically unbiased sample through random selection.

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4. A college president wants to find out which courses students consider to be of the most benefit to them. Which procedure would be most likely to produce a statistically unbiased sample?

✔ Correct Answer: b. surveying a random sample of students taken from the list of all students

Explanation:
Again, the gold standard for unbiased sampling is random selection from the entire population — here, all enrolled students.

- Option a (mail-in questionnaire) → voluntary response bias.
- Option c (first hundred on alphabetical list) → not random; may overrepresent names starting with early letters.
- Option d (web site questionnaire) → only reaches students who visit the site — likely not representative.

Only b uses proper random sampling from the full student body.

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5. A pollster wants to find out if citizens are satisfied with the city council. Which procedure would be most appropriate for obtaining a statistically unbiased sample?

✔ Correct Answer: b. surveying people whose names have been randomly chosen from the telephone book

Explanation:
While modern polling often uses random digit dialing or address-based sampling, among the given options, randomly selecting names from the telephone book is the closest to a random sample of the general public — assuming the phone book is relatively comprehensive.

- Option a (interviewing at shopping center) → convenience sample; biased toward shoppers, certain demographics.
- Option c (newspaper ad for mail-in responses) → voluntary response bias.
- Option d (mailing to utility customers) → excludes renters, low-income, etc.; not representative of all citizens.

Although telephone books may miss some populations (e.g., cell-only users), b is still the *most appropriate* among the choices for achieving an unbiased sample.

> ⚠️ Note: In real-world modern polling, telephone books are outdated, but since this is a basic stats worksheet, we assume it's treated as a reasonable sampling frame.

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✔ Final Answers:

1. d
2. c
3. a
4. b
5. b

Let me know if you’d like a printable version or further clarification!