Final answer:
The statement is true; a random sample is one where each member and geographic area has an equal chance of inclusion, ensuring the representativeness of the larger population.
Step-by-step explanation:
The statement that a random sample is a sample in which each member of the universe and each geographic area within it have a mathematically equal chance of being included is True. In random sampling, every individual in the targeted population has an equal probability of being selected. This ensures that the geographic and demographic distribution of the sample matches that of the population, which is important for the representativeness of the sample. Methods like simple random sampling, stratified sampling, and cluster sampling are designed to provide this equal chance. However, the use of technology and changes in communication mediums, such as the switch from landline phones to cell phones, have complicated the process, leading researchers to adapt their methods to maintain randomness and mitigate geographic bias.
Random samples are crucial because they are expected to be representative of the larger population, which is essential when drawing conclusions and making generalizations based on the sample. The validity and reliability of research findings are heavily dependent on the randomness and representativeness of the sample selected.