Assumptions:
a) Simple Random Samples and Independent Samples
b) Normal Difference or Large Sample
c) σ1 and σ2 Unknown
d) σ1 ≠ σ2 (Variances are unequal)


Step 1: Set up null and alternative hypotheses.

H0: μ1 = μ2                   (Note: H0: μ1 = μ2 ⇔ H0: μ1 - μ2 = 0)

H1: μ1 < μ2                   (Note: H1: μ1 < μ2 ⇔ H1: μ1 - μ2 < 0)



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 x̅1, x̅2, σ1, σ2, n1, and n2; and then calculate test statistic

x̅1 for population 1:           

s1 (population 1 standard deviation) =

n1 (sample size 1) =



x̅2 for population 2:           

s2 (population 2 standard deviation) =

n2 (sample size 2) =

Blank              (Note: From Step 1, we have H0: μ1 = μ2 ⇔ H0: μ1 - μ2 = 0; therefore, μ1 - μ2 = 0)





Step 4: Determine P-value

Using the test statistic in Step 3 as a t-score, we will find the left-tailed area corresponding to this t-score.
(Note: We use the t-distribution since the population stanadard deviations (σ1 and σ2) are unknown.)






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Calculating Mean and Standard Deviation

         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:           
.................... Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Column 9 Column 10 Column 11 Column 12 Column 13 Column 14 Column 15 Column 16 Column 17 Column 18 Column 19 Column 20 Column 21 Column 22 Column 23 Column 24 Column 25 Column 26 Column 27 Column 28 Column 29 Column 30 Column 31 Column 32 Column 33 Column 34 Column 35 Column 36 Column 37 Column 38 Column 39 Column 40 Column 41 Column 42 Column 43 Column 44 Column 45 Column 46 Column 47 Column 48 Column 49 Column 50
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