Question

Explain the difference between the body and the tail of a distribution. Which of these does the Standard Normal Distribution show?

Why do researchers have to use the distribution of sample means when conducting research?

Explain what probability is and why it’s useful for scientists .

Answer 1

The body of distribution covers the high-frequency points of data and covers up to 95-99% of data, while the tail focuses on low-frequency points, extreme values, and outliers in the data. It covers up to 5% of data. As you can see in the graph below, the blue shaded portion is the body, while the red-shaded portion is the tail.

The standard normal distribution encompasses both body and tail as can be seen from the graph above.

A sampling distribution is a probability distribution of a statistic that is obtained by drawing a large number of samples from a specific population.

Researchers use sampling distributions in order to simplify the process of statistical inference.

In reality, researchers aren’t always able to know or find their population parameter of interest with confidence. When this is the case, the researchers try to use estimation tactics to determine the population parameters with a high level of confidence

In order to estimate a population parameter, researchers take a sample of size n from the population of interest. They can then calculate a statistic from the sample that can be used to estimate the parameter.

However, because the sample being used is truly random, the statistic calculated for the specific sample might not be exactly the same as the original unknown parameter of interest.

This means that if the process was carried out again, and another random sample of size n was taken from the population, it is possible that the calculated statistic holds a different value than the calculated statistic that resulted from the first iteration of the process.

Hence, the researchers are forced to draw different random samples of the same size and plot the frequencies of different sample means. This plot would be called the sampling distribution. Such sampling distributions are used because, with adequate sample size, the Central Limit theorem will hold true and the sampling distribution will become approximately normal, allowing us to use its properties for easy estimation.

Thus, Sampling distributions are effective tools used by researchers to make estimates and inferences about a larger population of interest, based on the data that they have access to.

The probability is the likelihood of occurrence of different events resulting from a random experiment in terms of value ranging from 0 to 1. The probability is 0 for an impossible event and 1 for a certain event.

Probability is used by scientists in different aspects of data analysis proof claims that are not reviewed by statisticians. It is used in experiment data analysis, survey data analysis, and error estimation of such analysis. In Medicine, Scientists also use probability to predict outcome of various events possible due to a drug intake in humans.