diff --git a/tests/wrappers/test_normalize_observation.py b/tests/wrappers/test_normalize_observation.py
index 1fccc3b97..0fff7a995 100644
--- a/tests/wrappers/test_normalize_observation.py
+++ b/tests/wrappers/test_normalize_observation.py
@@ -1,9 +1,40 @@
 """Test suite for NormalizeObservation wrapper."""
+import numpy as np
 
+from gymnasium import spaces, wrappers
 from gymnasium.wrappers import NormalizeObservation
 from tests.testing_env import GenericTestEnv
 
 
+def test_normalization(convergence_steps: int = 1000, testing_steps: int = 100):
+    env = GenericTestEnv(
+        observation_space=spaces.Box(
+            low=np.array([0, -10, -5], dtype=np.float32),
+            high=np.array([10, -5, 10], dtype=np.float32),
+        )
+    )
+    env = wrappers.NormalizeObservation(env)
+
+    env.reset(seed=123)
+    env.observation_space.seed(123)
+    env.action_space.seed(123)
+    for _ in range(convergence_steps):
+        env.step(env.action_space.sample())
+
+    observations = []
+    for _ in range(testing_steps):
+        obs, *_ = env.step(env.action_space.sample())
+        observations.append(obs)
+    observations = np.array(observations)  # (100, 3)
+
+    mean_obs = np.mean(observations, axis=0)
+    var_obs = np.var(observations, axis=0)
+    assert mean_obs.shape == (3,) and var_obs.shape == (3,)
+
+    assert np.allclose(mean_obs, np.zeros(3), atol=0.15)
+    assert np.allclose(var_obs, np.ones(3), atol=0.15)
+
+
 def test_update_running_mean_property():
     """Tests that the property `_update_running_mean` freezes/continues the running statistics updating."""
     env = GenericTestEnv()
diff --git a/tests/wrappers/vector/test_normalize_observation.py b/tests/wrappers/vector/test_normalize_observation.py
index 773ca4037..3dab73b00 100644
--- a/tests/wrappers/vector/test_normalize_observation.py
+++ b/tests/wrappers/vector/test_normalize_observation.py
@@ -1,13 +1,12 @@
-"""Test suite for vector NormalizeObservation wrapper.."""
+"""Test suite for vector NormalizeObservation wrapper."""
 import numpy as np
 
 from gymnasium import spaces, wrappers
 from gymnasium.vector import SyncVectorEnv
-from gymnasium.vector.utils import create_empty_array
 from tests.testing_env import GenericTestEnv
 
 
-def thunk():
+def create_env():
     return GenericTestEnv(
         observation_space=spaces.Box(
             low=np.array([0, -10, -5], dtype=np.float32),
@@ -16,25 +15,52 @@ def thunk():
     )
 
 
-def test_against_wrapper(
-    n_envs=3,
-    n_steps=250,
+def test_normalization(
+    n_envs: int = 2, convergence_steps: int = 250, testing_steps: int = 100
+):
+    vec_env = SyncVectorEnv([create_env for _ in range(n_envs)])
+    vec_env = wrappers.vector.NormalizeObservation(vec_env)
+
+    vec_env.reset(seed=123)
+    vec_env.observation_space.seed(123)
+    vec_env.action_space.seed(123)
+    for _ in range(convergence_steps):
+        vec_env.step(vec_env.action_space.sample())
+
+    observations = []
+    for _ in range(testing_steps):
+        obs, *_ = vec_env.step(vec_env.action_space.sample())
+        observations.append(obs)
+    observations = np.array(observations)  # (100, 2, 3)
+
+    mean_obs = np.mean(observations, axis=(0, 1))
+    var_obs = np.var(observations, axis=(0, 1))
+    assert mean_obs.shape == (3,) and var_obs.shape == (3,)
+
+    assert np.allclose(mean_obs, np.zeros(3), atol=0.15)
+    assert np.allclose(var_obs, np.ones(3), atol=0.2)
+
+
+def test_wrapper_equivalence(
+    n_envs: int = 3,
+    n_steps: int = 250,
     mean_rtol=np.array([0.1, 0.4, 0.25]),
     var_rtol=np.array([0.15, 0.15, 0.18]),
 ):
-    vec_env = SyncVectorEnv([thunk for _ in range(n_envs)])
+    vec_env = SyncVectorEnv([create_env for _ in range(n_envs)])
     vec_env = wrappers.vector.NormalizeObservation(vec_env)
 
     vec_env.reset(seed=123)
+    vec_env.observation_space.seed(123)
     vec_env.action_space.seed(123)
     for _ in range(n_steps):
         vec_env.step(vec_env.action_space.sample())
 
-    env = wrappers.Autoreset(thunk())
+    env = wrappers.Autoreset(create_env())
     env = wrappers.NormalizeObservation(env)
     env.reset(seed=123)
     env.action_space.seed(123)
-    for _ in range(n_envs * n_steps):
+    for _ in range(n_steps // n_envs):
         env.step(env.action_space.sample())
 
     assert np.allclose(env.obs_rms.mean, vec_env.obs_rms.mean, rtol=mean_rtol)
@@ -42,29 +68,33 @@ def test_against_wrapper(
 
 
 def test_update_running_mean():
-    env = SyncVectorEnv([thunk for _ in range(2)])
+    env = SyncVectorEnv([create_env for _ in range(2)])
     env = wrappers.vector.NormalizeObservation(env)
 
     # Default value is True
     assert env.update_running_mean
 
-    obs, _ = env.reset()
+    env.reset()
     for _ in range(100):
         env.step(env.action_space.sample())
 
-    # Disable
+    # Disable updating the running mean
     env.update_running_mean = False
-    rms_mean = np.copy(env.obs_rms.mean)
-    rms_var = np.copy(env.obs_rms.var)
+    copied_rms_mean = np.copy(env.obs_rms.mean)
+    copied_rms_var = np.copy(env.obs_rms.var)
 
-    val_step = 25
-    obs_buffer = create_empty_array(env.observation_space, val_step)
-    env.action_space.seed(123)
-    for i in range(val_step):
-        obs, _, _, _, _ = env.step(env.action_space.sample())
-        obs_buffer[i] = obs
-
-    assert np.all(rms_mean == env.obs_rms.mean)
-    assert np.all(rms_var == env.obs_rms.var)
-    assert np.allclose(np.mean(obs_buffer, axis=(0, 1)), 0, atol=0.5)
-    assert np.allclose(np.var(obs_buffer, axis=(0, 1)), 1, atol=0.5)
+    # Continue stepping through the environment and check that the running mean is not effected
+    for i in range(10):
+        env.step(env.action_space.sample())
+
+    assert np.all(copied_rms_mean == env.obs_rms.mean)
+    assert np.all(copied_rms_var == env.obs_rms.var)
+
+    # Re-enable updating the running mean
+    env.update_running_mean = True
+
+    for i in range(10):
+        env.step(env.action_space.sample())
+
+    assert np.any(copied_rms_mean != env.obs_rms.mean)
+    assert np.any(copied_rms_var != env.obs_rms.var)