Assumptions:  a) Simple Random Sample         b) Normal Population or Large Sample         c) σ Unknown

Step 1: Set up null and alternative hypotheses.

H0: μ =

H1: μ >



Step 2: Input α (level of significance of hypothesis test).

α =     (Note: α = level of significance of hypothesis test   = probability of making Type I error.)

Step 3: Input x̅, n, s; and then calculate Test Statistic.



x̅ (sample mean) =

n (sample size) =

s = (sample standard deviation) =

Test Statistic =
    x̅ - μ     / s/n







Step 4: Find Critical Value

Critical Value = tα = t-score corresponding to the left-tailed area.






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Calculating Mean and Standard Deviation

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         How To Video


Input Data (separate data with semicolons; Example: 2;3;5;4;76):
If your data list is already in a table format (like an excel table), then paste table into textarea below:


Alternative p-value Method



Link: hypothesis testing using p-value method