"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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