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Hypotheses are assumptions about potential relationships. A test is conducted to either support (null hypothesis H0) or disprove (alternative hypothesis HA or H1) a suspicion with data. Through the tests, you choose between the two hypotheses. The alternative hypothesis suggests that a significant difference exists, while the null hypothesis states that no difference can be detected.
▪ H0: μ1 = μ2 oder σ1 = σ2
▪ HA: μ1 ≠ μ2 oder σ1 ≠ σ2
▪ Samples must be representative (randomly selected).
▪ To detect small differences, large sample sizes are needed.
Set the significance level. It is the maximum acceptable probability of error when accepting the alternative hypothesis. The standard is 0.05 (= 5%).
Select the appropriate test. For the mean, the t-test or ANOVA is suitable. For variance, the F-test or Levene's test is appropriate.
If 𝑝 > 𝛼, then the null hypothesis is accepted – no significant difference has been detected.
If 𝑝 < 𝛼, then the alternative hypothesis is accepted – a significant difference has been detected.
At our test company, which manufactures machines, we purchase screws from two suppliers.
We want to compare the strength of the screws by examining and testing them.
| Sample | Supplier A | Supplier B |
|---|---|---|
|
Mean - tensile strength |
768 N/mm² |
775 N/mm² |
|
Standard deviation - tensile strength |
37 N/mm² |
31 N/mm² |
|
Number of samples |
100 |
100 |
We formulate the hypothesis that the mean tensile strength of screws from both suppliers is the same (null hypothesis H0). The means of the two samples differ, but we know that there are always differences between two samples. The question is: At what point is the difference large enough to assume that the underlying populations are likely to differ?
The answer is provided by a two-sample t-test. From the spreadsheet, we read the test statistic as 0.149. The p-value is greater than the previously set significance level α of 0.05 (0.149 > 0.05). Therefore, we cannot say with 95% confidence that a difference exists. We assume that both suppliers are the same. You can see this in the summary provided.
At our company, which manufactures machines, we purchase screws from two suppliers.
We want to compare the strength of the screws by testing them.
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