The management group of a popular restaurant wanted to better understand their customers. They conducted a survey of 52 customers and recorded their responses to questions about their age, education level, income, job type etc. In particular, management felt that their customer base was getting younger and wanted to confirm this in order to tailor the 'dining experience' to the needs of this younger group. From a previous study, the average age of the customers was found to be 40 years. The survey revealed a sample mean of 38 years and a standard deviation of 8 years. Determine whether the average age of customers is significantly younger than in previous years.

1. State the null hypothesis in words AND statistical notation. 

2. State the alternate hypothesis in words AND statistical notation. 

3. Calculate the appropriate test statistic. 

4. What is your decision in terms of this example? 

5. What is your conclusion in relation to the original concern?