Question

Select two symbols that represent a statistic.

a.)
mu

b.)
x with bar on top

c.)
p with hat on top

d.)
p

e.)
sigma


need 2 answers

Answer 1

Answers: Choice B and Choice C

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Explanation:

The symbol $\mu$ or mu represents the population mean, which is a parameter.

The symbol $\sigma$ or sigma represents the population standard deviation, which is also a parameter. The same goes for the symbol p, without any hat on top, as it is the population proportion.

If something represents a population data item, then it's automatically a parameter. It might help to think both words "population" and "parameter" start with the letter P.

Based on those previous paragraphs, we can rule out choices A, D and E. Those three items are parameters. This leaves choices B and C as our final answers.

$\overline{x}$ or xbar is a sample statistic, and it represents an estimate of the population mean. Similarly, $\hat{p}$ or p-hat is the sample proportion and it represents an estimate of the population proportion. These are considered unbiased estimators.

Another example of an unbiased estimator is the variable s which represents the sample standard deviation and it estimates the value of sigma. All of these estimators have one thing in common: they are based on a sample, which in turn tries to predict what the corresponding population value is. In other words, the statistic's job is to estimate the parameter.

Below is a reference table for all of the items mentioned.