Test of Significance
• A test of significance is a formal procedure for comparing observed
data with a claim (also called a hypothesis), the truth of which is
being assessed.
• The claim is a statement about a parameter, like the population
proportion p or the population mean µ.
• The results of a significance test are expressed in terms of a
probability that measures how well the data and the claim agree.
Test of Significance using t-Test
• The difference between the sample mean or means is not significant,
if the calculated or t-statistic t0 value is lesser than the rejection
region value (t-critical) from the t-table. Therefore, the null
hypothesis H0 is accepted.
• The difference between the sample mean or means is significant, if
the calculated or t-statistic t0 value is greater than the rejection
region (t-critical) value from the t-table. Therefore, the null
hypothesis H0 is rejected.
t-Test Formulas
t-Test Example for 2, 4, 6, 8, 9, 10, 13 & 15 & x̄ = 56
• Student's two tailed t-test summary & example for test of significance
(hypothesis) for mean of small samples from population with unknown
variance by using t-statistic (t0)
• for dataset {2, 4, 6, 8, 9, 10, 13 & 15}, population mean μ = 56 and
critical value (te) from t-distribution table at 10% significance level for
the degrees of freedom ν = 7
• Step 1
• input parameters and values
• Data set value = 2, 4, 6, 8, 9, 10, 13 & 15
• Significance level (α) = 0.1
• population mean = 56
Step 5
Find expected te with level of significance α
= 0.1 , degrees of freedom ν = n - 1 = 7 from
two tailed t-distribution table
t e = 1.89
Inference
Step 4
To find t0, simplify the above expression
t0 > te
The null hypothesis H0 is rejected since t0 =
30.802 is greater than the critical value for
degrees of freedom te(6) = 1.89. Therefore,
there is significant difference between the
sample & population means.