Final answer:
The number of TC samples required is determined by the need for statistical representation, the sample size relative to the population, and adherence to specific sampling strategies and regulatory guidelines. A minimum of 30 samples is common if the population distribution is normal, with larger samples needed for non-normal distributions.
Step-by-step explanation:
The number of total coliform (TC) samples to be collected in a system depends on various factors. Statistical representation is crucial; it's important to collect enough samples to accurately represent the whole system or population being tested. The sample size, denoted as n, should be appropriately large with respect to the population to obtain reliable results from statistical analysis. For instance, if analyzing the quality of drinking water within a municipality, regulatory guidelines may dictate the minimum number of samples based on system size and population served.
Likewise, sampling strategy plays a role where simple random samples are independent, and each sample has an equal chance of being selected, offering a fair representation of the entire population. The rule of thumb is that the number of successes and failures in the sample count should both be at least five. Moreover, to avoid sampling bias and ensure a representative sample, it's suggested that the population should be at least 10 to 20 times the size of the sample. Considerations such as whether sampling is done with or without replacement can also affect the sample quantity requirement. For typical analytical purposes, a minimum of 30 samples or observations is often recommended if the population distribution is normal, while a larger sample may be required if the population is far from a normal distribution.