Q.6 - The Practice of Statistics for AP

Question

For each boldface number in Exercises 5 to 8, (1) state whether it is a parameter or a statistic and (2) use appropriate notation to describe each number; for example, p = 0.65 

Florida voters Florida has played a key role in recent presidential elections. Voter registration records show that 41% of Florida voters are registered as Democrats. To test a random digit dialing device, you use it to call 250 randomly chosen residential telephones in Florida. Of the registered voters contacted, 33% are registered, Democrats 

Step-by-Step Solution

Answer

1) The Given statement is a parameter

2)  The notation of the population proportion is  $p=0.41$  and the notation of the sample proportion is $\hat{p}=0.33.$$\hat{p}=0.33$

Part (1) Step 1: Given Information

Voters registered as Democrats $=41\%$

Registered Democrats of the voters contacted $=33\%$

Part (1) Step 2: Explanation

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The number of Democratic voters is an expressive metric of a population in this case. This implies that it is neither a statistic nor a parameter.

Also, the population proportion is:

$$\begin{gathered} p=41\% \\ =0.41 \end{gathered}$$

Hence, the statement is a parameter.

Part (2) Step 1: Given Information

Voters registered as Democrats $=41\%$

Registered Democrats of the voters contacted $=33\%$$=33\%$

Part (2) Step 2: Explanation

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The registered Democrats of the voters were approached for the sample via an expressive measure.

Also, the sample proportion is, 

$$\begin{gathered} \hat{p}=33\% \\ =0.33 \end{gathered}$$

and the population proportion is, 

$$\begin{gathered} p=41\% \\ =0.41 \end{gathered}$$

Hence, the notation of the population proportion is $p=0.41$ and the notation of the sample proportion is $\hat{p}=0.33$