True or false? a) Random samples only generate unbiased estimates of long-run pr

Question

True or false? a) Random samples only generate unbiased estimates of long-run proportions, not long-run means. b) Nonrandom samples are always biased. c) There is no way that a sample of 100 people can be representative of all adults living in the United States Sample of birds Argue whether or not you believe using a sample of birds which visit a bird feeder in your yard the next 50 birds that visit) may or may not yield biased estimates based on the variable being measured/research question being investigated in each of the following situations. Using the proportion of finches out of 50 th t visit the bur feeder to esu nate the proportion of finches among all bids that live near your backyard b) Using the proportion of finches (out of 50) that are at the bird feeder when another finch is also at the bird feeder to estimate the proportion of the time that finches prefer to eat with other finches Using the proportion of male birds (out of 50) that visit the bird feeder to estimate the proportion of male birds among all birds that live near your backyard d) Using the proportion of male birds that visit the bird feeder to estimate the proportion of male birds that typically visit bird feeders

Explanation / Answer

Question 2.1.5

a)

Random samples only generate unbiased estimates for long run PROPORTIONS NOT long run means.

This statement is true.

Using the definition of sample:

A random sample is a sample in which each member of the population has an equal chance of being selected.

Random samples generate unbiased estimates of the population mean, whereas non random samples may not be unbiased.

b)

To answer this we need to know what bias means. In statistical terms bias is a difference between the expected value of an estimator and the true value in the population of whatever it is we are trying to estimate.

So bias only makes sense in terms of estimating something. A sample cannot be biased in itself, only the estimators derived from it.

The estimators will only be biased if the parameter we are trying to estimate is linked to the likelihood of selection of an individual population member into our sample.

So if tall people are more likely to be sampled, then our sample will yield biased estimates of height. If happy people are more likely to respond, then our estimates of mood will be biased.

c)

There is no way that a sample of 100 people can be representative of all adults living in the United States.

This statement is false.

Using the definition of sample:

A sample is a subset of the population selected to represent the whole population.

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