State what is wrong in each of the following scenarios. 1. A sampling distributi

Question

State what is wrong in each of the following scenarios.

1. A sampling distribution describes the distribution of some characteristic in a population.

(a) The sampling distribution describes the distribution of all the characteristics of a population, not just one.

(b) The sampling distribution describes the variation of the characteristic of a sample. A characteristic of a population does not vary; it is a fixed number.

(c) The population distribution describes the variation of the characteristic of a population. A characteristic of a sample does not vary; it is a fixed number.

2. A statistic will have a large amount of bias whenever it has high variability.

(a) Statistics are never biased because they rely on empirical data; the variability does not matter.

(b) Bias and variability are independent; any combination of high/low bias and high/low variability is possible.    

(c) Statistics are always highly biased regardless of the variability.

(d) Bias is always high when variability is low, not when variability is high.

3. The variability of a statistic based on a small sample from a population will be the same as the variability of a large sample from the same population.

(a) For a given population, variability decreases with increasing sample size, so the variability for the large sample will be smaller.

(b) For a given population, variability increases with increasing sample size, so the variability for the large sample will be larger.    

(c) For a given population, variability is lowest when the sample size is moderate; a small or large sample size means that the variability will be larger.

(d) For a given population, variability is independent of sample size, so there is no way to know how the variability will change for the large sample.

Explanation / Answer

1.

Correct option:

(b) Thesampling distribution describes the variation of the characteristic of asample. A characteristic of a population does not vary ; it isa fixed value.

2.

Correct option:

(b) Bias and variability are independent; any combination of high/ low biasand high/ low variability ispossible.

3.

Correct option:

(a) For a given population, variability decreases with increasing sample size, so the variability for the large sample will be smaller.

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