A confidence interval around an estimated mean expresses:
Correct Answer
D) The range likely to contain the true value at a stated probability
Why this is correct: The correct answer, 'The range likely to contain the true value at a stated probability,' defines a confidence interval. It quantifies the uncertainty in a sample-based estimate (like a mean) by providing a range within which the true population parameter is expected to fall, with a specified level of confidence (e.g., 95%). This aligns with the original explanation that it 'converts sample uncertainty into a stated range' and avoids overstating precision. Why the other choices are wrong: 'The correlation between two variables' describes a measure of association, not a range around an estimate. 'The exact value the parameter must take' is incorrect because a confidence interval expresses a range of plausible values, not a single exact point. 'The total number of individual observations included in the sample' refers to the sample size (n), not a probabilistic range. Exam tip: Remember, a confidence interval is about the precision of an estimate, not the data points themselves. It's a range, not a single number or a measure of relationship.
Why This Is the Correct Answer
Why this is correct: The correct answer, 'The range likely to contain the true value at a stated probability,' defines a confidence interval. It quantifies the uncertainty in a sample-based estimate (like a mean) by providing a range within which the true population parameter is expected to fall, with a specified level of confidence (e.g., 95%). This aligns with the original explanation that it 'converts sample uncertainty into a stated range' and avoids overstating precision. Why the other choices are wrong: 'The correlation between two variables' describes a measure of association, not a range around an estimate. 'The exact value the parameter must take' is incorrect because a confidence interval expresses a range of plausible values, not a single exact point. 'The total number of individual observations included in the sample' refers to the sample size (n), not a probabilistic range. Exam tip: Remember, a confidence interval is about the precision of an estimate, not the data points themselves. It's a range, not a single number or a measure of relationship.
More appraisal-statistical-methods Questions
A price index rises from 100 to 121 over two years. What compound annual rate does this represent?
A sample of four sales drawn from a market with 200 annual transactions is:
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
An appraiser includes both 'total room count' and 'bedroom count' as independent variables in a regression model estimating single-family home sale prices. The variance inflation factor (VIF) for 'bedroom count' is calculated as 12.3. What is the most appropriate appraisal action based on this result?
An appraiser runs a regression of sale price on GLA, age, and a binary variable for 'renovated' (1 = yes, 0 = no). The estimated coefficient for 'renovated' is $18,400 with a standard error of $6,200 and a t-statistic of 2.97. Assuming a two-tailed test at Ξ± = 0.05 and 42 degrees of freedom, what conclusion is supported regarding the market's recognition of renovations?
To validate the functional form of a regression model used for adjustments, an appraiser plots residuals against predicted values and observes a clear inverted-U pattern. What does this pattern indicate, and what is the most defensible corrective action?
A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
What does it mean to validate a regression model?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?