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"quantity"exercise: Sampling
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Questions 1:
Survivorship bias is most likely an example of which bias?
A、Sample selection
B、Data mining
C、 Look-ahead
Questions 2:
A sample of 438 observations is randomly selected from a population. The mean
of the sample is 382, and the standard deviation is 14. Based on Chebyshev’s
inequality, the endpoints of the interval that must contain at least 88.89% of the
observations are closest to:
A 、340 and 424.
B 、396 and 480.
C 、354 and 410
View answer resolution
【Answer to question 1】A
【analysis】
A is correct. Sample selection bias often results when a lack of data availability leads to certain data being excluded from the analysis. Survivorship bias is an example of sample selection bias.
B is incorrect. Data mining bias relates to the overuse of the same or related data, i.e., searching for pattern. And survivorship bias is not an example of data mining bias.
C is incorrect. Look-ahead bias exists if the model uses data not available to the analyst at the time the analyst act on the model. Survivorship bias is not an example of look-ahead bias
【Answer to question 2】A
【analysis】
A is correct. According to Chebyshev’s inequality, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 – 1/k2 for all k >1. For k = 3, that proportion is 1 – 1/32, which is 88.89%. The lower endpoint is, therefore, the mean (382) minus 3 times 14 (the standard deviation), and the upper endpoint is 382 plus 3 times 14 (i.e., 340 and 424, respectively).
C is incorrect; it is based on 2 standard deviations, not 3: 382 – 2 × 14 = 354 and 382 + 2 × 14 = 410.
B is incorrect; it centers the interval around the number of observations (438) rather than the mean (382)
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