The ________ is a hypothesis-testing procedure in which there are two separate groups at people tested and the population variance is not known
The hypothesis-testing procedure you are referring to is called the independent samples t-test. This test is used to compare the means of two separate groups when the population variance is unknown.
To conduct an independent samples t-test, follow these steps:
1. State the null and alternative hypotheses: Start by defining the null hypothesis (H0) and alternative hypothesis (H1) based on the research question. The null hypothesis typically assumes that there is no significant difference between the means of the two groups, while the alternative hypothesis suggests that there is a significant difference.
2. Collect data: Gather the required data for the two groups you want to compare. Make sure the samples are independent, meaning that the individuals in one group do not overlap with the individuals in the other group.
3. Calculate the sample means: Find the mean of each group by summing up the values and dividing by the sample size.
4. Calculate the sample standard deviations: Determine the standard deviation of each group using the formula for the sample standard deviation:
s = √((∑(x - x̄)²) / (n - 1))
where x is the value, x̄ is the mean, and n is the sample size.
5. Calculate the test statistic: Calculate the t-value using the following formula:
t = (x̄₁ - x̄₂) / √((s₁² / n₁) + (s₂² / n₂))
Where x̄₁ and x̄₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes of the two groups.
6. Determine the degrees of freedom: Calculate the degrees of freedom for the test using the formula:
df = (s₁² / n₁ + s₂² / n₂)² / ((s₁² / n₁)² / (n₁ - 1) + (s₂² / n₂)² / (n₂ - 1))
7. Find the critical value or p-value: Consult a t-table or use statistical software to find the critical value corresponding to the desired significance level (e.g., 0.05). Alternatively, you can calculate the p-value associated with the observed t-value.
8. Make a decision: Compare the calculated t-value with the critical value or p-value. If the calculated t-value falls in the critical region or the p-value is smaller than the predetermined significance level, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
9. Draw conclusions: Based on the decision made in the previous step, interpret the results within the context of the problem and draw appropriate conclusions.
Remember, conducting a proper independent samples t-test requires careful consideration of assumptions, such as normality and independence, and it's important to correctly interpret the results in order to draw meaningful conclusions.