The government claims that the average age of Californians is 34 years. Joe hypothesizes that the average age of the population of California is not equal to 34 years. He records a sample mean equal to 37 and states the hypothesis as $\mu=34$ vs $\mu \neq 34$. What type of test should Joe do? Two-tailed test Right-tailed test Left-tailed test Joe should not do any of the types of tests listed.

Step 1 ：Joe is testing whether the average age of the population of California is not equal to 34 years. This means he is looking for a difference in either direction - either the average age is less than 34 or it is greater than 34.

Step 2 ：This suggests that a two-tailed test would be appropriate. A two-tailed test is used when we do not specify the direction of the difference we are expecting.

Step 3 ：In this case, Joe is not specifying whether he expects the average age to be lower or higher than 34, he is simply stating that he expects it to be different.

Step 4 ：Therefore, a two-tailed test is the appropriate choice.

Step 5 ：Final Answer: \(\boxed{\text{Two-tailed test}}\).