As you wish to use Minitab to conduct a hypothesis test for two populations, I'll guide you through the steps to perform a two-sample t-test. The test will compare the means of two independent samples to determine if there is statistical evidence that the associated population means are significantly different. We will use an alpha level of 5% for our test (α = 0.05).
First, let's state our null and alternative hypotheses:
- Null hypothesis (H0): μ1 = μ2 (The two population means are equal)
- Alternative hypothesis (H1): μ1 ≠ μ2 (The two population means are not equal)
Here are the steps to perform the two-sample t-test in Minitab:
1. Open Minitab and enter your data.
- Enter the values for Sample 1 into one column (e.g., C1).
- Enter the values for Sample 2 into another column (e.g., C2).
2. To perform the hypothesis test, click on "Stat" in the menu bar.
3. Choose "Basic Statistics" and then select "2-Sample t..."
4. A new window will appear. Specify the columns where the data for the two samples was entered. You can do this by selecting C1 for Sample 1 and C2 for Sample 2.
5. Under the "Options" button, ensure that the confidence level is set to 95% (which corresponds to an alpha level of 5%).
6. Since you are not given information about the population variances being equal or not, you can consider checking the "Assume equal variances" option. Alternatively, you can leave this unchecked, and Minitab will perform a Welch's t-test, which does not assume equal variances.
7. Click "OK" to run the test.
Minitab will then provide the output, which includes the sample means, the t-statistic, degrees of freedom, and the p-value.
Interpretation:
- If the p-value is less than α (0.05), you reject the null hypothesis, suggesting that there is a statistically significant difference in the population means.
- If the p-value is greater than α, you fail to reject the null hypothesis, suggesting that there is no statistically significant difference between the population means.
Using the p-value and the sample means, you can determine which sample has a lower or higher average.
Also remember:
- A p-value lower than 0.05 indicates that there is less than a 5% probability of observing the data if the null hypothesis were true and thus you reject the null hypothesis in favor of the alternative.
- A p-value higher than 0.05 suggests that there is insufficient evidence to reject the null hypothesis.
You should now have enough information to determine which population has a lower average based on the results provided by Minitab.