In statistical analysis, a normal curve represents the normal or standard distribution of data from a large sample size (Hogg, 2004). A normal curve is generally represented by a symmetrical bell-shaped distribution in a graph. A normal curve or distribution represents a sample population that has a mean of 0 and a standard deviation value of 1 (Mendenhall and Sincich, 2006). These standard scores are also called z-scores, which represent standardized data that have been had the mean value taken away and have been separated by the standard deviation.
The distribution observed in a normal curve can be employed to test a hypothesis about a mean. This may be performed sampling the members of a population being studied and extracting the mean itself. By taking samples from this distribution, one may determine whether the sample mean age is different from the real mean age. This test is also referred to as the two-tailed test, wherein the extremes of the normal curve represent the proportion of cases by 0. 0. 5 or less (Hogg, 2005).
This means that the scores at the low and high extremes of the normal curve may be different from the established mean of the sample population. This also provides that 95% of the sample population follows the average mean that has been calculated by simple calculation. The normal distribution that is observed in a normal curve follows the assumption that the variable of interest is well-distributed in the population. There are z tests that are considered as parametric tests that assume the setting of normally distributed data.
On the other hand, those that do not require an assumption regarding the distribution of data are referred to a non-parametric statistics.
References Hogg RV (2004): Introduction to mathematical statistics, 6th ed. New York: Prentice-Hall. 692 pages. Hogg RV (2005): Probability and statistical inference, 7th ed. New York: Prentice-Hall. 752 pages. Mendenhall W and Sincich T (2006): Statistics for engineering and the sciences, 5th ed. New York: Prentice-Hall. 1072 pages.
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