1. Which probability distribution should be used when sampling takes place from a small population where the probability of success does not remain the same for each trial? Why?
The central limit theorem holds that the totals (and therefore the means) of random samples will be normally distributed no matter what the distribution in the population is like, provided only that the samples are large enough. In most instances where inferential statistics are applied in hypothesis testing, population distributions are unknown. Therefore, the central limit theorem assumes a high-level of importance in hypothesis testing. Thus, one may expect normally distributed data in large samples more so than in small samples. If the sample size is less than 30 and if the standard deviation is not known, but it also is possible to make a rational assumption that the sample is characterized by a near-normal distribution, it is best to use the t distribution in place of the normal distribution. The justification is that the t distribution is a continuous distribution that shares the characteristics of the normal distribution (i.e., it is bell-shaped and symmetrical). Discrete random data also may be analyzed within the context of Poisson distribution. Poisson distribution requires that (a) the length of the observation period is fixed in advance of data collection, (b) the events counted must occur at a constant average rate, and (c) the events occurring in disjoint intervals are statistically independent.
2. What are some differences between discrete and continuous data?
Discrete data are characterized by natural categories. Continuous data, however, do not fall into natural categories. Discrete data, thus, are susceptible to counting (i.e., how many dogs and how many cats and how many rats are in New York. Continuous data, in contrast to discrete data, may be any value on a scale of measurement. Thus, discrete data are counted, while conti...