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

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Explanation:

The symbol [tex]\mu[/tex] or mu represents the population mean, which is a parameter.

The symbol [tex]\sigma[/tex] 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.

[tex]\overline{x}[/tex] or xbar is a sample statistic, and it represents an estimate of the population mean. Similarly, [tex]\hat{p}[/tex] 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.

A parameter, represented by the symbol mu, is the population mean.

Thus, The population standard deviation, another parameter, is denoted by the letter sigma. The symbol p, which stands for population proportion and has no hat on top, is equivalent.

Something is inherently a parameter if it represents a population data item. It could be helpful to remember that the words "parameter" and "population" both begin with the letter P.

We can eliminate options A, D, and E based on the sentences above. These three things are constraints and parameter. This leaves B and C as our only remaining options. In a similar manner, or p-hat is the sample proportion and it and population.

Thus, A parameter, represented by the symbol mu, is the population mean.

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(c)tyrannical and imperious

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