3. The manager of a gym claimed that the mean age of its customers is 30 years. A random sample of 75 customers is taken and their ages have a mean of 28.2 years and a standard deviation, \(s\), of 8.5 years.
- Stating your hypotheses clearly and using a 10\% level of significance, test whether or not the manager's claim is supported by the data.
- Explain the relevance of the Central Limit Theorem to your calculation in part (a).
- State an additional assumption needed to carry out the test in part (a).