Suppose you are conducting a lab experiment to compare the means of two independent groups with approximately normal distributions and unknown but equal variances. Which of the following statistical tests should you use?

• A. Paired samples $t$-test
• B. Independent samples $t$-test
• C. $\chi ²$ test for independence
• D. One-way $ANOVA$

Answer: (B)

Verified step by step guidance

1. Identify the type of data and groups involved: Here, you have two independent groups with approximately normal distributions and unknown but equal variances.
2. Understand the goal: You want to compare the means of these two independent groups to see if there is a significant difference between them.
3. Recall the assumptions and appropriate tests: For two independent groups with normal distributions and equal variances, the Independent samples t-test is the suitable choice.
4. Eliminate other options: The Paired samples t-test is used for related or matched samples, the Chi-square test for independence is for categorical data, and One-way ANOVA is used when comparing means across three or more groups.
5. Conclude that the Independent samples t-test is the correct statistical test to use in this scenario.