# What is a sample?

Whereas a population is the entire group of objects that a certain researcher is interested in; a sample is defined as the fixed number of objects you get from a certain population. For example, Amelia wants to know if red flowers attract bees more than yellow flowers. In order to prove this assumption, Amelia takes a sample of a red flower (e. g. rose) and a yellow flower (e. g. a sunflower). There are lots of flowers that are red and yellow in color. Amelia could not afford to obtain every red and yellow flower in order to prove her assumption.

Thus, it is practical for her to take a “representative” from all the red flowers and a “representative” from all the yellow flowers. Taking “representatives” from the entire population, you could now call these “samples”. It is essential to remember that the fundamental assumption underlying most of the theory of sampling is random sampling. This consists of the selection of individuals from the population in such a way that each individual of the population has an equal chance of being selected. The process of such selection is called random sampling.

The aim of the theory of sampling is to get as much information as possible, ideally all the information about the population from which the sample has been drawn. From the parent population, in particular, we would like to estimate the parameters of the population or specify the limits or ranges within which the population parameters are expected to lie with a specified degree of confidence. At work, we use sampling to prove or test something. For example, you want to determine if the new time management scheme will be beneficial to cut the costs on your company.

So, as a manager, you could take some employees to undergo this new time management scheme in order to see if the new process is suitable for both the company and the employees. 2. What are the differences between the binomial and normal distributions? What are the similarities between the binomial and normal distributions? The normal distribution is the most commonly encountered distribution range in science. Random variables in normal distribution should be capable of assuming any value on the real number line, though this requirement is often not applied.

For example, height at a given age for a given gender in a given racial group is adequately described by a normal random variable even though heights must be positive. A continuous random variable X, taking all real values in the range. The graph of variables with normal distribution is a symmetrical, bell-shaped curve, centered at its expected mean value. Typically, a binomial random variable is the number of successions in a series of trials in binomial distributions.

For example, the number of ‘heads’ occurring when a coin is tossed 50 times; thus a discrete random variable X is said to follow a binomial distribution with parameters n and p. However, the probability trials must meet the following requirements: a. the total number of trials is fixed in advance; b. there are just two outcomes of each trial; success and failure; c. the outcomes of all the trials are statistically independent; d. all the trials have the same probability of success. The similarity of normal and binomial distributions rely on the use of random variables as part of the data and their values could be both positive and negative.

3. What do confidence intervals represent? Give an example of the use of a confidence interval. Before a simple research question could be resolved like, for instance, “What is the mean number of flowers that one person can remember? ” it is necessary to specify the population of people to which this question will be addressed. The researcher could be interested in, for example, children under the age of 12 and girls. For the present example, assume the researcher is interested in all girls aged 9. Once the population is specified, the next step is to take a random sample from it.

In this example, let’s say that a sample of 10 girls is drawn and each student’s memory tested. The way to estimate the mean of all girls would be to compute the mean of the 10 girls in the sample. Indeed, the sample mean is an unbiased estimate of ? , the population mean. However, it will certainly not be a perfect estimate. By chance it is bound to be at least either a little bit too high or a little bit too low. For the estimate of ? to be of value, one must have some idea of how precise it is. That is, how close to ? is the estimate likely to be?

So we use the confidence intervals to determine how close would be the unbiased estimate we have in our sample to the values that is indicated in the population mean. If the number of flowers that the 10 girls remembered were: 4, 4, 5, 5, 5, 6, 6, 7, 8, 9 then the estimated value of ? would be 5. 9 and the 95% confidence interval would range from 4. 71 to 7. 09. The wider the interval, the more confident you are that it contains the parameter you are interested in. The 99% confidence interval is therefore wider than the 95% confidence interval and extends from 4. 19 to 7. 61.