Q. 28 - Elementary Statistics

Question

Gasoline Prices, The U.S. Energy Information Administration reports weekly figures on retail gasoline prices in Weekly Retail Garo Line and Diesel Prices, Every Monday, retail prices for all three grades of gasoline are collected by telephone from a sample of approximately 800 retail gasoline outlets out of a total of more than 100,000 retail gasoline outlets. For the 800 stations sampled in September 16, 2013, the mean price per gallon for unleaded regular gasoline was $\backslash (3.547$.

• a. Is the mean price given here a sample mean or a population mean? Explain your answer.
• b. What letter or symbol would you use to designate the mean of $\backslash )3.547$?
• c. Is the mean price given here a statistic or a parameter? Explain your answer.

Step-by-Step Solution

Answer

Ans: 

Part (a). The mean price given here is a sample mean $\$3.547$

Part (b). The symbol that is used to designate the mean of $\$3.547$ is $\overline{x}$.

Part (c). The given mean price is a statistic 

Step 1. Given information:

•  Retail gasoline prices in Weekly Retail Garo Line and Diesel Prices 
•  $800$ retail gasoline outlets out of a total of more than $100,000$ retail gasoline outlets
•  The mean price per gallon for unleaded regular gasoline was $\$3.547$

Step 2. Solving Part (a):

The sample is the subset of the population from which data are actually collected.

Here, 800 gasoline service stations are taken as the sample.

Here, the mean price $(\$3.547)$ per gallon for unleaded regular gasoline is obtained from a sample of $800$ gasoline service stations.

Therefore, the mean price given here is a sample mean.

Step 3. Solving Part (b):

The symbol that is used to designate the mean of $\$3.547$ is $\overline{x}$.

Step4. Solving Part (c):

When the same measure of the entire population is calculated for a sample from that population, then it is called a statistic.

That is, the sample statistic is the number that describes the sample that is obtained from summarizing the raw data.

Therefore, it can be concluded that the given mean price is a statistic.