Let's analyze and solve the questions in the document systematically.

Question 1: Sampling for Predicting Election Outcomes

Which option is most effective for predicting the outcome of the election, and why?

The options are:

• (a) 100 completed surveys handed out randomly through the city.
• (b) 100 phone calls made to different parts of the city.
• (c) 100 people interviewed at a neighborhood-watch party.
• (d) 100 surveys completed by children at a middle school.

Answer: The best option is (a) because it uses random sampling, which is crucial to eliminate bias and ensure a representative sample of the city's population.

• Why not others?
  • (b), while covering different parts of the city, may not be random, as phone lists might miss certain groups of people.
  • (c) focuses on a specific group (neighborhood-watch attendees) and lacks diversity.
  • (d) is skewed, as children aren't eligible voters.

Question 2: Testing Defective Calculators

The task involves analyzing the results of testing calculators and making estimates.

(a) After the first test, would it be fair to say that none of the calculators were broken? Why or why not?

No, it would not be fair. Testing only 20 calculators is a very small sample size relative to the shipment of 10,000 calculators. It's possible that the test missed defective units due to randomness or clustering of defects.

(b) Whose statement is more accurate: Sami (2%) or Sima (1.5%)?

To determine accuracy:

• In the second test, 100 calculators were tested and 2 were broken. $\text{Defect Rate} = \frac{2}{100} = 0.02 \, \text{or } 2\%.$
• In the third test, 15 out of 1000 calculators were broken: $\text{Defect Rate} = \frac{15}{1000} = 0.015 \, \text{or } 1.5\%.$

Both statements are based on small samples. Sami's estimate (2%) is slightly more consistent with the smaller sample size tested earlier.

(c) Estimate the number of defective calculators in the shipment.

Using an average defect rate (combining data from all tests):

• Test results:
  • 2/100 = 2%.
  • 15/1000 = 1.5%.

Assuming a defect rate around 1.75% (average of 2% and 1.5%): $\text{Estimated Defective Calculators} = 10,000 \times 0.0175 = 175.$

Approximately 175 calculators in the shipment might be defective.

Question 3: Sampling for Gelman’s Rent-All

(a) What type of sample is this?

This is a voluntary response sample, as individuals can choose to participate by filling out the sheets.

(b) Pros and cons of this method?

• Pros:

  • Easy and inexpensive to conduct.
  • No interviewer bias since respondents self-select.

• Cons:

  • Likely to suffer from response bias (only people with strong opinions are likely to participate).
  • May not represent the population of the plaza accurately.

Follow-Up

Would you like further clarification on any of the questions? Let me know!

Related Questions:

1. What are some methods to ensure unbiased sampling for surveys?
2. How does sample size impact the accuracy of defect estimates?
3. What is the difference between random sampling and voluntary response sampling?
4. How do outliers affect defect-rate estimates in manufacturing?
5. Can we calculate a confidence interval for the defect estimate? How?

Tip: Always strive for randomness and an adequate sample size to minimize bias and improve accuracy in statistical surveys.