Using the county auditor's list of households the researcher randomly selected 100 homes and contacted the residents. Of the 100 homes it was found that 62 had cable television.
Which of the following are true?
The population of interest is the proportion of all homes in Franklin County Ohio that have cable television.
The population of interest is all homes in Franklin County Ohio.
The parameter of interest is the proportion of all homes in Franklin County Ohio that have cable television.
The parameter of interest is the proportion of the 100 homes that have cable television.
The parameter of interest is the county auditors list of households.
The parameter of interest is 62%.
The population of interest is the proportion of the 100 homes that have cable television.
The population of interest is the county auditors list of households.
The correct options are:
- The population of interest is the proportion of all homes in Franklin County Ohio that have cable television.
- The parameter of interest is the proportion of all homes in Franklin County Ohio that have cable television.
To determine the correct answers, we need to understand the concepts of population and parameter in the context of this question.
In statistical analysis, a population refers to the entire group of individuals or items that the researcher wants to study. In this case, the population of interest is all homes in Franklin County Ohio.
A parameter, on the other hand, is a characteristic or measure that describes a population. It is usually derived from data collected from a sample. In this case, the parameter of interest is the proportion of all homes in Franklin County Ohio that have cable television.
The sample in this scenario consists of 100 randomly selected homes, and out of those, 62 were found to have cable television. Therefore, the sample proportion is 62/100 = 0.62 or 62%.
However, the sample is used to estimate the population parameter. So, the proportion of homes with cable television in the sample is not the parameter of interest, rather it is an estimate of the parameter.
Hence, the correct answers are that the population of interest is the proportion of all homes in Franklin County Ohio that have cable television, and the parameter of interest is the proportion of all homes in Franklin County Ohio that have cable television.