When comparing two independent samples with unknown and unequal variances, which of the following statements is NOT true?

• A. The pooled variance formula $s^2=\frac{n_1-1}{{s^2}_1}$ is appropriate for estimating the standard error.
• B. The degrees of freedom are calculated using a specific formula that accounts for unequal variances.
• C. The two samples are assumed to be independent.
• D. $\mathrm{Welch}\text{'}s$ t-test is commonly used in this scenario.

Answer: (A)

Verified step by step guidance

1. Understand the context: When comparing two independent samples with unknown and unequal variances, the appropriate test to use is Welch's t-test, which does not assume equal variances.
2. Recall that the pooled variance formula is used when the variances of the two samples are assumed to be equal. Since the variances are unequal here, the pooled variance formula is NOT appropriate.
3. Recognize that the degrees of freedom in Welch's t-test are calculated using a special formula that adjusts for the unequal variances, rather than using the simpler formula for equal variances.
4. Confirm that the assumption of independence between the two samples is still required regardless of whether variances are equal or unequal.
5. Summarize that the incorrect statement is the one claiming the pooled variance formula is appropriate, because it applies only when variances are equal, not when they are unequal.