Mixed Deck — All FAST Topics Flashcards

Which of the following is the primary goal of the least squares method in regression?

Answer: Minimize the sum of squared residuals

OLS finds the line (or hyperplane) that minimizes the sum of squared differences between observed and predicted values.

A team of 4 workers completes a task in 6 days. How many days would it take 8 workers to complete the same task?

Answer: 3 days

Doubling the workers halves the time, so 6 ÷ 2 = 3 days.

What does 'demand characteristics' refer to in an experiment?

Answer: Cues that lead participants to guess the study's purpose and alter their behavior accordingly

Demand characteristics are cues in the experimental setting that hint at the study's purpose, causing participants to change their behavior to match perceived expectations.

What does a 95% confidence interval mean?

Answer: If we repeated the sampling many times, 95% of the intervals would contain the true parameter

A 95% confidence interval means that the procedure used will capture the true parameter 95% of the time across repeated samples.

Which of the following is an important skill for analytical problem-solving?

Answer: Logical reasoning and pattern recognition

Logical reasoning allows individuals to assess facts, identify patterns, and make well-informed decisions based on evidence.

A project budget of $150,000 was overspent by 12%. What was the actual expenditure?

Answer: $168,000

Actual = $150,000 × 1.12 = $168,000.

What is the difference between independent and dependent events?

Answer: Independent events do not affect each others probability; dependent events do

Independent events have no influence on each other, while the occurrence of a dependent event changes the probability of the other.

Sam is older than Tom. Tom is older than Kate. Who is the youngest?

Answer: Kate

The chain Sam > Tom > Kate places Kate as the youngest.

When a researcher uses quota sampling, the goal is to:

Answer: Ensure the sample matches the population on key characteristics without random selection

Quota sampling sets target numbers for subgroups to mirror population characteristics, but selection within quotas is non-random.

Which of the following fractions is greatest?

Answer: 5/11

Converting to decimals: 3/7≈0.429, 5/11≈0.455, 7/15≈0.467, 9/20=0.45 — 7/15 is the greatest.

Which of the following would INCREASE the width of a confidence interval?

Answer: Increasing the confidence level from 95% to 99%.

Higher confidence requires a larger critical value, which increases the margin of error and widens the interval.

Which of the following is the strongest evidence that a conclusion is well-supported?

Answer: Multiple independent, peer-reviewed studies consistently reach the same conclusion

Independent replication across rigorous studies is the gold standard of evidence, reducing the chance that results are due to bias or error.

Why is critical thinking crucial in problem-solving?

Answer: It enables objective analysis and conclusion generation

Critical thinking enables individuals to objectively analyze information, challenge assumptions, and generate well-supported conclusions.

A test has 5 multiple-choice questions each with 4 options. If a student guesses randomly, what is the probability of getting all 5 correct?

Answer: 1/1024

Each question has a 1/4 chance of being correct, so all 5 correct = (1/4)^5 = 1/1024.

A data table shows that as advertising spending increases by $1,000, sales increase by $5,000. A researcher concludes that advertising causes sales. What flaw exists in this reasoning?

Answer: Correlation does not prove causation

A consistent relationship between two variables (correlation) does not establish that one causes the other — a third factor could explain both.

If 5 workers complete a job in 12 days, how many days will 10 workers take to complete the same job?

Answer: 6 days

Workers × days is constant; 5 × 12 = 10 × d, so d = 6 days.

What does it mean if a confidence interval for a difference includes zero?

Answer: The difference is not statistically significant at that confidence level

Including zero means we cannot rule out no difference, so the result is not statistically significant at the given confidence level.

Two statements: 'All managers are employees' and 'Some employees are part-time.' Which conclusion is valid?

Answer: Some managers may be part-time

'Some managers may be part-time' is the only valid conclusion since the overlap between part-time employees and managers is possible but not confirmed.

A sample of 36 scores has a mean of 80 and standard deviation of 12. The standard error of the mean is:

Answer: 2

Standard error = s / √n = 12 / √36 = 12 / 6 = 2.

In hypothesis testing, what does 'fail to reject H₀' mean?

Answer: There is insufficient evidence to conclude H₀ is false

Failing to reject H₀ means the data do not provide enough evidence against it — it does not prove H₀ is true.