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3.1 Estimation, Confidence Intervals & Errors — Test 1
Q1. A point estimate of a population parameter is:✓ A single value used to estimate the parameter
Q2. A confidence interval is:✓ A range of values likely to contain the true parameter
Q3. A 95% confidence interval means that:✓ If sampling were repeated, about 95% of such intervals would contain the parameter
Q4. The null hypothesis (H0) in a statistical test typically states that:✓ There is no effect or no difference
Q5. A Type I error occurs when:✓ A true null hypothesis is rejected (false positive)
Q6. A Type II error occurs when:✓ A false null hypothesis is not rejected (false negative)
Q7. The power of a statistical test is defined as:✓ 1 − β (the probability of correctly rejecting a false null hypothesis)
Q8. For a fixed confidence level, increasing the sample size makes a confidence interval:✓ Narrower
Q9. For a fixed sample, increasing the confidence level (e.g. from 95% to 99%) makes the interval:✓ Wider
Q10. The margin of error of a confidence interval represents:✓ The half-width added to and subtracted from the point estimate
Q11. The probability of committing a Type I error is denoted by, and controlled through:✓ The significance level α
Q12. An estimator differs from an estimate in that an estimator is:✓ The rule or formula, while the estimate is the resulting value
Q13. The alternative hypothesis (H1) in a test states that:✓ There is an effect or a difference
Q14. A confidence interval is constructed using the point estimate and the:✓ Standard error (and a confidence coefficient)
Q15. Reducing the chance of a Type I error by lowering α, with sample size fixed, tends to:✓ Increase the chance of a Type II error
Q16. Common confidence levels used in practice are:✓ 90%, 95% and 99%
Q17. Hypothesis testing assesses evidence by:✓ Determining whether sample data are consistent with the null hypothesis
Q18. An unbiased estimator is one whose:✓ Expected value equals the true parameter
Q19. A wider confidence interval, all else equal, indicates:✓ Greater uncertainty about the parameter
Q20. Match each concept with its description and select the correct option.✓ A-iv, B-ii, C-i, D-iii