Step one: State null hypothesis and alternative hypothesis in symbolic form.
Usually the hypothesis concerns the value of a population parameter.
How to express null hypothesis and alternative hypothesis in symbolic form
Identify H1 first. If the original claim of the question uses words such as “greater, larger,
increased, improved and so on”, use “>” for H1. If it uses words such as “less, decreased,
smaller and s o on”, apply “<” for H1. If words such as “the same, change,
different/difference and so on” appear in the cl aim, use “≠” for H1. The oppos ite symbol
wil l be used for H0. (Note: For MATH 1257, always use “=” for H0.)
Step two: Compute the test statistics value.
Step three: Identify the critical value or the P-value by the tables.
Be aware of how many tails exist when you l ook up the critical value in the tabl e. If the
symbols “>,<,≥,≤” are used in H1, it is one-tailed. If the symbol “≠” is used in H1, two-
tailed.
The significance levels 1%, 5% and 10% are commonly used.
Confidence Level + Significance Level = 1 i.e. Confidence Level = 1 – Signi ficance Level
Therefore, when si gnificance l evel equals 1%, 5% or 10%, confidence level equals 99%,
95% or 90% respectively. The corresponding critical z values are shown as follows:
Significance Level
Confidence Level
Critical z Value
1%
99%=0.99
2.575
5%
95%=0.95
1.96
10%
90%=0.90
1.645
Step four: Draw a graph included the test statistics value, the critical value
and the critical region(s) or compare the P-value with the significance level
α. And then make a conclusion of the hypothesis.
Four Steps of Hypothesis Testing
