# Basic Statistics and Data Analysis

#### Lecture notes, MCQS of Statistics

Mostly used statistical tables, Z-table, t-table, F-table, chi-square table etc.

# Standard Normal table

A standard normal table, also called the unit normal table or Z-table, is a table for the values of Φ calculated mathematically, and these are the values from the cumulative normal distribution function. Standard normal table is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety (families) of normal distributions, so it is common practice to convert a normal to a standard normal and then use the standard normal table to find the required probabilities (area under the curve).

Standard normal curve is symmetrical in nature, so the table can be used for values going in any of direction, for example a negative 0.45 or positive 0.45 has an area of 0.1736.

The Standard Normal distribution is used in various hypothesis testing procedures such as tests on single means, the difference between two means, and tests on proportions. The Standard Normal distribution has a mean of 0 and a standard deviation of 1.

The values inside the given table represent the areas under the standard normal curve for values between 0 and the relative z-score.

The table value for Z is 1 minus the value of the cumulative normal distribution.

For example, the value for 1.96 is P(Z>1.96) = .0250.