a city planner is studying the need for affordable housing in the citys urban planning department. he learned from the census of all 80,571 households in the city that the median family income is $55,000, with an average of 3.5 persons-per-household, and 82% live in a single household unit. previously, the planner had surveyed a group of 500 randomly selected households in the city. the surveyed households had a median family income of $47,000, an average of 4.2 persons-per-household, and 77% lived in a single household unit.
(a) for city planner’s survey, identify the population and the sample.
population: select
sample: select
(b) choose whether each number described below is a parameter or a statistic for the city planner’s survey.
number parameter statistic
the 82% of all the households in the city that live in a single household unit ○ ○
the $47,000 median family income of the group of randomly selected households ○ ○
the average of 3.5 persons-per-household of all the households in the city ○ ○

Question

a city planner is studying the need for affordable housing in the citys urban planning department. he learned from the census of all 80,571 households in the city that the median family income is $55,000, with an average of 3.5 persons-per-household, and 82% live in a single household unit. previously, the planner had surveyed a group of 500 randomly selected households in the city. the surveyed households had a median family income of $47,000, an average of 4.2 persons-per-household, and 77% lived in a single household unit.
(a) for city planner’s survey, identify the population and the sample.
population: select
sample: select
(b) choose whether each number described below is a parameter or a statistic for the city planner’s survey.
number	parameter	statistic
the 82% of all the households in the city that live in a single household unit	○	○
the $47,000 median family income of the group of randomly selected households	○	○
the average of 3.5 persons-per-household of all the households in the city	○	○

Accepted Answer

# Brief Explanations:
- **(a)**
    - **Population**: The population is the entire group of interest. Here, it is all $80,571$ households in the city.
    - **Sample**: The sample is a subset of the population. In this case, it is the $500$ randomly selected households.
- **(b)**
    - **Parameter**: A parameter is a characteristic of the population. The median family income of $\$55,000$, the average of $3.5$ persons - per - household, and $82\%$ living in a single household unit (from the census of all households) are parameters as they describe the entire population of $80,571$ households in the city.
    - **Statistic**: A statistic is a characteristic of the sample. The median family income of $\$47,000$, the average of $4.2$ persons - per - household, and $77\%$ living in a single household unit (from the sample of $500$ households) are statistics as they describe the sample of $500$ households.

# Answer:
- **(a)**
    - Population: All $80,571$ households in the city.
    - Sample: The $500$ randomly selected households.
- **(b)**
    - Parameter: The $82\%$ of all the households in the city that live in a single household unit, the average of $3.5$ persons - per - household of all the households in the city,  the median family income of $\$55,000$ (from the census of all households).
    - Statistic: The $77\%$ of the surveyed households that lived in a single household unit, the average of $4.2$ persons - per - household of the surveyed households, the median family income of $\$47,000$ (from the sample of $500$ households).

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