Question

In the 2000 presidential election, three candidates split the vote as follows:

Bush 47.9% Gore 48.4% Nader 2.7%
We will consider a vote for Al Gore a "success." We can look back and select a random sample of 50 voters from the 2000 election and count the number of those who voted for Gore. Suppose in that sample 23 voted for Gore.

Which of the following is correct?

a 0.46 and 0.484 are statistics

b 50 and 23 are statistics and 0.484 is a
parameter

c 23 and 0.46 are statistics and 0.484 is a
parameter

Answer 1

c 23 and 0.46 are statistics and 0.484 is a parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

`\hat p_{Gore]=(X)/(n)=(23)/(50)=0.46`

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.

Explanation:

Previous concepts

A parameter is any "numerical quantity that characterizes a given population or some aspect of it". For this case we are interested on proportions and we denote the population proportion by
`p`

A statistic is "used to estimate the value of a population parameter". In other words is just an estimation of the population parameter of interest. Four our case the sample proportion denoted by
`\hat p` represent the statistic for this case.

Solution for the problem

a 0.46 and 0.484 are statistics

False. 0.484 is not an statistic since it's the outcome from the original population and would represent the parameter "proportion of people who vote for Gore"

b 50 and 23 are statistics and 0.484 is a parameter

False. The sample size is not an statistic is just a value selected in order to calculate the statistic.

c 23 and 0.46 are statistics and 0.484 is a parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

`\hat p_{Gore]=(X)/(n)=(23)/(50)=0.46`

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.