If the null hypothesis is rejected by a one-way analysis of variance, further analysis are necessary to determine which population means differ from the others.

Incorrect.

This answer choice is **grammatically** incorrect. The **singular subject** *analysis* does not agree with the **plural verb** *are*.

*Analysis* is a confusing **subject**. It ends with -s, which might make us think of it as a **plural subject**, but it is, in fact, **singular** (its plural form is *analyses*).

Incorrect.

While this answer choice corrects the **original Subject Verb Agreement** mistake, it creates a new one: the **singular subject** *hypothesis* does not agree with the **plural verb** *are*.

*Hypothesis* is a confusing **subject**. It ends with -s, which might make us think of it as a **plural subject**, but it is, in fact, **singular** (its plural form is *hypotheses*).

Well done! In this answer choice, a **singular verb** correctly follows both *hypothesis* and *analysis*.

This answer choice corrects the **original Subject Verb Agreement** mistake and is **grammatically** correct. However, it is **stylistically** flawed. Replacing the **single word** *differ* with the **two-word** phrase *are different* creates **redundancy**.

Incorrect.

This answer choice repeats the **original** mistake. The **singular subject** *analysis* does not agree with the **plural verb** *are*.

*Analysis* is a confusing **subject**. It ends with -s, which might make us think of it as a **plural subject**, but it is, in fact, **singular** (its plural form is *analyses*).

In addition, this answer choice creates another **Subject Verb Agreement** mistake. The **plural subject ***h**ypotheses* does not agree with the **singular verb** *is*.

hypothesis is rejected by a one-way analysis of variance, further
analysis are necessary to determine which population means differ

hypothesis are rejected by a one-way analysis of variance, further
analysis is necessary to determine which population means differ

hypothesis is rejected by a one-way analysis of variance, further
analysis is necessary to determine which population means differ

hypothesis is rejected by a one-way analysis of variance, further
analysis is necessary to determine which population means are different

hypotheses is rejected by a one-way analysis of variance, further
analysis are necessary to determine which population means differ