Certain eggs are stated to have reduced cholesterol content, with an average of only 2.5% cholesterol. A concerned health group wants to test whether the claim is true. The group believes that more cholesterol may be found, on the average, in the eggs. A random sample of 100 eggs reveals a sample average content of 5.2% cholesterol, and a sample standard deviation of 2.8%. Does the health group have cause for action?