Z-Test for Normal Distribution

When a claim is made about a population — for instance, that a new drug is effective, or that a process meets some target — a hypothesis test is used to judge how likely that claim is to be true, based on sample data. Several such tests exist, including the F-test, chi-square test, t-test and Z-test; the Z-test is the one used with normally distributed data.

Before applying a Z-test, a few conditions need to be checked:

• the sample size should be greater than $30$;
• the data points should be independent of one another;
• the data should be randomly selected, with every member of the population equally likely to be chosen;
• as far as possible, sample sizes being compared should be equal.

Standard Normal (Z) Table

The table below is the standard normal cumulative table: each entry is the area under the standard normal curve to the left of $z$, that is $\Phi(z)=P(Z\le z)$, for $z$ from $0.00$ to $3.69$. Read the whole-and-first-decimal part of $z$ from the row and the second decimal from the column — for example $\Phi(1.20)=0.8849$ is row $1.2$, column $0.00$. For a negative value, use the symmetry of the curve: $\Phi(-z)=1-\Phi(z)$.